Algebra | IAF AFCAT Past Year Papers PDF Download

 Page 1


B-30 Algebra
Algebra
3
1. In an examination a candidate has to get 35% of total marks
to pass. In one paper he gets 62 out of 150 and in the second
35 out of 150. How many marks should he get out of 200
marks in the third paper to pass ? [2011-I]
(a) 61 (b) 68
(c) 70 (d) 78
2. The salary of A & B together amounts to ` 2000. A spends
95% of his salary and B 85% of his salary . If their savings
are same what is the salary of A ? [2011-I]
(a) ` 750 (b) ` 1250
(c) ` 1500 (d) ` 1600
3. Out of the 1000 inhabitants of a town, 60% are male of whom
20% are literate. If, amongst all the inhabitants, 25% are
literate, then what percentage of the females of the town are
literate ? [2011-I]
(a) 2 2.5 (b) 32.5
(c) 27.5 (d) 37.5
4. A trader mixes 26 kg of rice at ` 20 per kg with 30 kg rice of
another variety costing ` 36 per kg. If he sells the mixture at
` 30 per kg his profit will be- [2011-I]
(a) –7% (b) 5%
(c) 8% (d) 10%
5. The difference between the cost price and sale price is `
240. If the profit is 20%, the selling price is [2011-I]
(a) ` 1200 (b) ` 1440
(c) ` 1800 (d) ` 2440
6. Samant bought a microwave oven and paid 10% less than
Maximum Retail Price(MRP). He sold it with 30% profit
on his purchase cost. What percentage of profit did he earn on
MRP ? [2011-I]
(a) 17% (b) 20%
(c) 27% (d) 32%
7. ` 800 becomes ` 956 in 3 years at a certain rate of interest.
If the rate of interest is increased by 4% what amount will
` 800 become in 3 years ? [2011-I]
(a) ` 1020 (b) ` 1052
(c) ` 1282 (d) ` 1080
8. How much time will it take for an amount of ` 450 to gain
` 81 as interest, if rate of interest is 4.5% p.a on simple
interest ? [2011-I]
(a) 4.5 years (b) 3.5 years
(c) 5 years (d) 4 years
9. At what rate of annual simple interest will `10000 double in
15 years ? [2011-I]
(a) 5.5% (b) 8%
(c) 6.67% (d) 7.25%
10. What percentage of profit should be added in the cost price
of an item so as to gain a profit of 33% after allowing 5%
discount to the customer ? [2011-II]
(a) 45 (b) 40
(c) 52 (d) 48
11. If the manufacturer gains 10%, the wholesale dealer gains
15% and the retailer gains 25%, find the cost of production
of a table. The retail price of table is ` 1265 [2011-II]
(a) ` 800 (b) ` 1000
(c) ` 950 (d) ` 1180
12. A loss of 19% on a shirt gets converted into a profit of 17%
when the selling price is increased by ` 162. What is the
cost price of the shirt ? [2011-II]
(a) ` 540 (b) ` 450
(c) ` 600 (d) ` 360
13. In an examination 75% of the total students passed in English
and 65% passed in Mathematics, while 15% failed in English
as well as Mathematics. If a total of 495 candidates who
passed in both exams. Find the total number of students
who appeared in the exam. [2011-II]
(a) 8 50 (b) 9 00
(c) 1000 (d) 1050
14. When the price of a product was increased by 15%, the
number of items sold was decreased by 20%. What was the net
effect ? [2011-II]
(a) 10% gain (b) 6% loss
(c) 8% loss (d) 4% gain
15. A mixture of 40 litres of milk and water contains 10% water.
How much water should be added to this mixture so that the
new mixture contains 20% water ? [2011-II]
(a) 4 litres (b) 5 litres
(c) 6.5 litres (d) 7.5 litres
16. A certain sum of money becomes three times of itself
in 20 years at simple interest. In how many years will
the initial sum become double at the same rate of simple
interest ? [2011-II]
(a)8 (b) 10
(c) 12 (d) 14
17. Ram borrows ` 8000 at 12% p.a. simple interest and Mohan
borrows ` 9100 at 10% p.a. simple interest. In how many years
will their borrowed amounts (debt) be equal ? [2011-II]
(a) 18 (b) 2 0
(c) 22 (d) 2 4
Page 2


B-30 Algebra
Algebra
3
1. In an examination a candidate has to get 35% of total marks
to pass. In one paper he gets 62 out of 150 and in the second
35 out of 150. How many marks should he get out of 200
marks in the third paper to pass ? [2011-I]
(a) 61 (b) 68
(c) 70 (d) 78
2. The salary of A & B together amounts to ` 2000. A spends
95% of his salary and B 85% of his salary . If their savings
are same what is the salary of A ? [2011-I]
(a) ` 750 (b) ` 1250
(c) ` 1500 (d) ` 1600
3. Out of the 1000 inhabitants of a town, 60% are male of whom
20% are literate. If, amongst all the inhabitants, 25% are
literate, then what percentage of the females of the town are
literate ? [2011-I]
(a) 2 2.5 (b) 32.5
(c) 27.5 (d) 37.5
4. A trader mixes 26 kg of rice at ` 20 per kg with 30 kg rice of
another variety costing ` 36 per kg. If he sells the mixture at
` 30 per kg his profit will be- [2011-I]
(a) –7% (b) 5%
(c) 8% (d) 10%
5. The difference between the cost price and sale price is `
240. If the profit is 20%, the selling price is [2011-I]
(a) ` 1200 (b) ` 1440
(c) ` 1800 (d) ` 2440
6. Samant bought a microwave oven and paid 10% less than
Maximum Retail Price(MRP). He sold it with 30% profit
on his purchase cost. What percentage of profit did he earn on
MRP ? [2011-I]
(a) 17% (b) 20%
(c) 27% (d) 32%
7. ` 800 becomes ` 956 in 3 years at a certain rate of interest.
If the rate of interest is increased by 4% what amount will
` 800 become in 3 years ? [2011-I]
(a) ` 1020 (b) ` 1052
(c) ` 1282 (d) ` 1080
8. How much time will it take for an amount of ` 450 to gain
` 81 as interest, if rate of interest is 4.5% p.a on simple
interest ? [2011-I]
(a) 4.5 years (b) 3.5 years
(c) 5 years (d) 4 years
9. At what rate of annual simple interest will `10000 double in
15 years ? [2011-I]
(a) 5.5% (b) 8%
(c) 6.67% (d) 7.25%
10. What percentage of profit should be added in the cost price
of an item so as to gain a profit of 33% after allowing 5%
discount to the customer ? [2011-II]
(a) 45 (b) 40
(c) 52 (d) 48
11. If the manufacturer gains 10%, the wholesale dealer gains
15% and the retailer gains 25%, find the cost of production
of a table. The retail price of table is ` 1265 [2011-II]
(a) ` 800 (b) ` 1000
(c) ` 950 (d) ` 1180
12. A loss of 19% on a shirt gets converted into a profit of 17%
when the selling price is increased by ` 162. What is the
cost price of the shirt ? [2011-II]
(a) ` 540 (b) ` 450
(c) ` 600 (d) ` 360
13. In an examination 75% of the total students passed in English
and 65% passed in Mathematics, while 15% failed in English
as well as Mathematics. If a total of 495 candidates who
passed in both exams. Find the total number of students
who appeared in the exam. [2011-II]
(a) 8 50 (b) 9 00
(c) 1000 (d) 1050
14. When the price of a product was increased by 15%, the
number of items sold was decreased by 20%. What was the net
effect ? [2011-II]
(a) 10% gain (b) 6% loss
(c) 8% loss (d) 4% gain
15. A mixture of 40 litres of milk and water contains 10% water.
How much water should be added to this mixture so that the
new mixture contains 20% water ? [2011-II]
(a) 4 litres (b) 5 litres
(c) 6.5 litres (d) 7.5 litres
16. A certain sum of money becomes three times of itself
in 20 years at simple interest. In how many years will
the initial sum become double at the same rate of simple
interest ? [2011-II]
(a)8 (b) 10
(c) 12 (d) 14
17. Ram borrows ` 8000 at 12% p.a. simple interest and Mohan
borrows ` 9100 at 10% p.a. simple interest. In how many years
will their borrowed amounts (debt) be equal ? [2011-II]
(a) 18 (b) 2 0
(c) 22 (d) 2 4
Algebra
18. Reena took a loan of ` 1200 with simple interest for a certain
numbers of years. The number years are same as the interest
rate. If she has paid ` 432 as interest at the end of the loan
period, what was the rate of interest ? [2011-II]
(a) 3.6 (b) 6
(c) 12 (d) None of these
19. Hari’s income is 20% more than Madhu’s income. Madhu’s
income is less than Hari’s income by [2012-I]
(a) 15% (b) 16.66 %
(c) 2 0% (d) 22.25%
20. A sum of money lent out at simple interest doubled itself in
20 years. In how many years will it triple itself ? [2012-I]
(a) 28 yrs (b) 30 yrs
(c) 40 yrs (d) 35 yrs
21. One litre of water is evaporated from 6 litres of a solution
containing 5% salt. The percentage of salt in the remaining
solution is [2012-I]
(a) 16% (b) 5%
(c) 4% (d) 6%
22. A shopkeeper professes to sell all things at a discount of
10% but increases the selling price of each article by 20%.
His gain on each article is [2012-I]
(a) 6% (b) 8%
(c) 1 0% (d) 12%
23. If the selling price of an article is 4/3
rd
 of its cost price, the
profit in transaction is [2012-I]
(a) 16.75% (b) 20.50%
(c) 25.50% (d) 33.33%
24. If selling price is doubled, the profit triples. Find the profit
percent. [2012-I]
(a) 66.66 (b) 1 00
(c) 105.33 (d) 1 20
25. Srinivasan invests two equal amounts in two banks giving
10% and 12% rate of interest respectively. At the end of
year the interest earned is ` 1650. Find the sum invested in
each. [2012-II]
(a) `  8500 (b) `  15000
(c) `  7500 (d) `  17,000
26. The simple interest on sum of money is 1/9 of the sum. The
number of years is numerically equal to the rate percent per
annum. The rate percent per annum is [2012-II]
(a) 3.33 (b) 5
(c) 6.66 (d) 10
27. A sum of ` 10.000 is lent partly at 8% and the remaining at
10% per annum, If the yearly  interest on the average is
9.2%. the money lent at 10% is [2012-II]
(a) `  6000 (b) `  5500
(c) `  5000 (d) `  4500
28. In an election between two candidates, 60% of the voters
cast their votes, out of which 4% of the votes were declared
invalid. A candidate got 7344 votes which were 75% of the
total valid votes. Find the total number of votes enrolled in
that election. [2012-II]
(a) 1700 (b) 17590
(c) 17000 (d) 7344
29. If the price of kerosene be raised by 9%, find how much
percent a house holder must reduce his consumption of
kerosene so that not to increase his expenditure [2012-II]
(a) 9% (b) 8.25%
(c) 9% (d) 9.25%
30. Sixty five pupils from a school entered for an examination
and 80% of them passed. Another school entered 10 more
pupils than the first school and four more pupils passed.
The % of pass in the second school was [2012-II]
(a) 75% (b) 84%
(c) 72% (d) 74.6%
31. Calculate the amount on ` 1250 for 2 years at 4% per annum.
compounded yearly. [2012-II]
(a) ` 676 (b) ` 1352
(c) ` 1778 (d) ` 255
32. A sum of ` 3200 is lent out into two parts, one at 6% and
another at 4%. If the total annual income is ` 176, find the
money lent at 6%. [2012-II]
(a) `  2400 (b) ` 800
(c) `  1600 (d) ` 3200
33. Srinivasan invests two equal amounts in two banks
giving 8% and 12% rate of interest respectively. At the end
of year the interest earned is ` 1500. Find the sum invested
in each. [2013-I]
(a) ` 8500 (b) ` 15000
(c) ` 7500 (d) ` 17000
34. The simple interest accrued on a sum of money at the end of
four years is 1/5
th
 of its principal. What is the rate of interest
per annum ? [2013-I]
(a) 4% (b) 5%
(c) 6% (d) Inadequate data
35. A sum of ` 2600 is lent out into two parts, one at 9% and
another at 7%. If the total annual income is ` 206, find the
money lent at 7%. [2013-I]
(a) ` 1400 (b) ` 900
(c) ` 1600 (d) ` 1200
36. In an election between two candidates, 70% of the voters
cast their votes, out of which 2% of the votes were declared
invalid. A candidate got 7203 votes which was 60% of the
total valid votes. Find the total number of voters enrolled in
that election. [2013-I]
(a) 18050 (b) 17500
(c) 17000 (d) 7203
37. If the price of kerosene be raised by 11%, find by how much
percent a house holder must reduce his consumption of
kerosene so as not to increase his expenditure ? [2013-I]
(a) 1 1% (b) 9.9%
(c) 11.09% (c) 8.25%
38. 75 pupils from a school appeared for an examination and
80% of them passed. Another school entered 10 more pupils
than the first school and five pupils less than the first school
passed. The pass % of in the second school was [2013-I]
(a) 75% (b) 84%
(c) 72% (d) 64.7%
39. Calculate the amount on ` 1875 for 2 years at 4% per annum,
compounded yearly. [2013-I]
(a) ` 676 (b) ` 776
(c) ` 1778 (d) ` 2028
40. If x varies as y and x = 8 when y = 15 then the values of x
when y = 10 is [2013-I]
(a)5 (b) 15/8
(c) 8/15 (d) 16/3
Page 3


B-30 Algebra
Algebra
3
1. In an examination a candidate has to get 35% of total marks
to pass. In one paper he gets 62 out of 150 and in the second
35 out of 150. How many marks should he get out of 200
marks in the third paper to pass ? [2011-I]
(a) 61 (b) 68
(c) 70 (d) 78
2. The salary of A & B together amounts to ` 2000. A spends
95% of his salary and B 85% of his salary . If their savings
are same what is the salary of A ? [2011-I]
(a) ` 750 (b) ` 1250
(c) ` 1500 (d) ` 1600
3. Out of the 1000 inhabitants of a town, 60% are male of whom
20% are literate. If, amongst all the inhabitants, 25% are
literate, then what percentage of the females of the town are
literate ? [2011-I]
(a) 2 2.5 (b) 32.5
(c) 27.5 (d) 37.5
4. A trader mixes 26 kg of rice at ` 20 per kg with 30 kg rice of
another variety costing ` 36 per kg. If he sells the mixture at
` 30 per kg his profit will be- [2011-I]
(a) –7% (b) 5%
(c) 8% (d) 10%
5. The difference between the cost price and sale price is `
240. If the profit is 20%, the selling price is [2011-I]
(a) ` 1200 (b) ` 1440
(c) ` 1800 (d) ` 2440
6. Samant bought a microwave oven and paid 10% less than
Maximum Retail Price(MRP). He sold it with 30% profit
on his purchase cost. What percentage of profit did he earn on
MRP ? [2011-I]
(a) 17% (b) 20%
(c) 27% (d) 32%
7. ` 800 becomes ` 956 in 3 years at a certain rate of interest.
If the rate of interest is increased by 4% what amount will
` 800 become in 3 years ? [2011-I]
(a) ` 1020 (b) ` 1052
(c) ` 1282 (d) ` 1080
8. How much time will it take for an amount of ` 450 to gain
` 81 as interest, if rate of interest is 4.5% p.a on simple
interest ? [2011-I]
(a) 4.5 years (b) 3.5 years
(c) 5 years (d) 4 years
9. At what rate of annual simple interest will `10000 double in
15 years ? [2011-I]
(a) 5.5% (b) 8%
(c) 6.67% (d) 7.25%
10. What percentage of profit should be added in the cost price
of an item so as to gain a profit of 33% after allowing 5%
discount to the customer ? [2011-II]
(a) 45 (b) 40
(c) 52 (d) 48
11. If the manufacturer gains 10%, the wholesale dealer gains
15% and the retailer gains 25%, find the cost of production
of a table. The retail price of table is ` 1265 [2011-II]
(a) ` 800 (b) ` 1000
(c) ` 950 (d) ` 1180
12. A loss of 19% on a shirt gets converted into a profit of 17%
when the selling price is increased by ` 162. What is the
cost price of the shirt ? [2011-II]
(a) ` 540 (b) ` 450
(c) ` 600 (d) ` 360
13. In an examination 75% of the total students passed in English
and 65% passed in Mathematics, while 15% failed in English
as well as Mathematics. If a total of 495 candidates who
passed in both exams. Find the total number of students
who appeared in the exam. [2011-II]
(a) 8 50 (b) 9 00
(c) 1000 (d) 1050
14. When the price of a product was increased by 15%, the
number of items sold was decreased by 20%. What was the net
effect ? [2011-II]
(a) 10% gain (b) 6% loss
(c) 8% loss (d) 4% gain
15. A mixture of 40 litres of milk and water contains 10% water.
How much water should be added to this mixture so that the
new mixture contains 20% water ? [2011-II]
(a) 4 litres (b) 5 litres
(c) 6.5 litres (d) 7.5 litres
16. A certain sum of money becomes three times of itself
in 20 years at simple interest. In how many years will
the initial sum become double at the same rate of simple
interest ? [2011-II]
(a)8 (b) 10
(c) 12 (d) 14
17. Ram borrows ` 8000 at 12% p.a. simple interest and Mohan
borrows ` 9100 at 10% p.a. simple interest. In how many years
will their borrowed amounts (debt) be equal ? [2011-II]
(a) 18 (b) 2 0
(c) 22 (d) 2 4
Algebra
18. Reena took a loan of ` 1200 with simple interest for a certain
numbers of years. The number years are same as the interest
rate. If she has paid ` 432 as interest at the end of the loan
period, what was the rate of interest ? [2011-II]
(a) 3.6 (b) 6
(c) 12 (d) None of these
19. Hari’s income is 20% more than Madhu’s income. Madhu’s
income is less than Hari’s income by [2012-I]
(a) 15% (b) 16.66 %
(c) 2 0% (d) 22.25%
20. A sum of money lent out at simple interest doubled itself in
20 years. In how many years will it triple itself ? [2012-I]
(a) 28 yrs (b) 30 yrs
(c) 40 yrs (d) 35 yrs
21. One litre of water is evaporated from 6 litres of a solution
containing 5% salt. The percentage of salt in the remaining
solution is [2012-I]
(a) 16% (b) 5%
(c) 4% (d) 6%
22. A shopkeeper professes to sell all things at a discount of
10% but increases the selling price of each article by 20%.
His gain on each article is [2012-I]
(a) 6% (b) 8%
(c) 1 0% (d) 12%
23. If the selling price of an article is 4/3
rd
 of its cost price, the
profit in transaction is [2012-I]
(a) 16.75% (b) 20.50%
(c) 25.50% (d) 33.33%
24. If selling price is doubled, the profit triples. Find the profit
percent. [2012-I]
(a) 66.66 (b) 1 00
(c) 105.33 (d) 1 20
25. Srinivasan invests two equal amounts in two banks giving
10% and 12% rate of interest respectively. At the end of
year the interest earned is ` 1650. Find the sum invested in
each. [2012-II]
(a) `  8500 (b) `  15000
(c) `  7500 (d) `  17,000
26. The simple interest on sum of money is 1/9 of the sum. The
number of years is numerically equal to the rate percent per
annum. The rate percent per annum is [2012-II]
(a) 3.33 (b) 5
(c) 6.66 (d) 10
27. A sum of ` 10.000 is lent partly at 8% and the remaining at
10% per annum, If the yearly  interest on the average is
9.2%. the money lent at 10% is [2012-II]
(a) `  6000 (b) `  5500
(c) `  5000 (d) `  4500
28. In an election between two candidates, 60% of the voters
cast their votes, out of which 4% of the votes were declared
invalid. A candidate got 7344 votes which were 75% of the
total valid votes. Find the total number of votes enrolled in
that election. [2012-II]
(a) 1700 (b) 17590
(c) 17000 (d) 7344
29. If the price of kerosene be raised by 9%, find how much
percent a house holder must reduce his consumption of
kerosene so that not to increase his expenditure [2012-II]
(a) 9% (b) 8.25%
(c) 9% (d) 9.25%
30. Sixty five pupils from a school entered for an examination
and 80% of them passed. Another school entered 10 more
pupils than the first school and four more pupils passed.
The % of pass in the second school was [2012-II]
(a) 75% (b) 84%
(c) 72% (d) 74.6%
31. Calculate the amount on ` 1250 for 2 years at 4% per annum.
compounded yearly. [2012-II]
(a) ` 676 (b) ` 1352
(c) ` 1778 (d) ` 255
32. A sum of ` 3200 is lent out into two parts, one at 6% and
another at 4%. If the total annual income is ` 176, find the
money lent at 6%. [2012-II]
(a) `  2400 (b) ` 800
(c) `  1600 (d) ` 3200
33. Srinivasan invests two equal amounts in two banks
giving 8% and 12% rate of interest respectively. At the end
of year the interest earned is ` 1500. Find the sum invested
in each. [2013-I]
(a) ` 8500 (b) ` 15000
(c) ` 7500 (d) ` 17000
34. The simple interest accrued on a sum of money at the end of
four years is 1/5
th
 of its principal. What is the rate of interest
per annum ? [2013-I]
(a) 4% (b) 5%
(c) 6% (d) Inadequate data
35. A sum of ` 2600 is lent out into two parts, one at 9% and
another at 7%. If the total annual income is ` 206, find the
money lent at 7%. [2013-I]
(a) ` 1400 (b) ` 900
(c) ` 1600 (d) ` 1200
36. In an election between two candidates, 70% of the voters
cast their votes, out of which 2% of the votes were declared
invalid. A candidate got 7203 votes which was 60% of the
total valid votes. Find the total number of voters enrolled in
that election. [2013-I]
(a) 18050 (b) 17500
(c) 17000 (d) 7203
37. If the price of kerosene be raised by 11%, find by how much
percent a house holder must reduce his consumption of
kerosene so as not to increase his expenditure ? [2013-I]
(a) 1 1% (b) 9.9%
(c) 11.09% (c) 8.25%
38. 75 pupils from a school appeared for an examination and
80% of them passed. Another school entered 10 more pupils
than the first school and five pupils less than the first school
passed. The pass % of in the second school was [2013-I]
(a) 75% (b) 84%
(c) 72% (d) 64.7%
39. Calculate the amount on ` 1875 for 2 years at 4% per annum,
compounded yearly. [2013-I]
(a) ` 676 (b) ` 776
(c) ` 1778 (d) ` 2028
40. If x varies as y and x = 8 when y = 15 then the values of x
when y = 10 is [2013-I]
(a)5 (b) 15/8
(c) 8/15 (d) 16/3
Algebra
41. A sum of ` 10,000 is lent partly at 6% and the remaining at
10% p.a. If the yearly interest on the average is 9.2%, the
money lent at 10% is [2013-I]
(a) ` 2000 (b) ` 8500
(c) ` 5000 (d) ` 8000
42. An article costs ` 50 presently . The rate of inflation is 300%.
What will be cost of this article after two years ? [2014-I]
(a) ` 200 (b) ` 600
(c) ` 800 (d) ` 1000
43. A dishonest shopkeeper professes to sell his groceries at
his cost price, but uses a false weight of 900 grams for each
kilogram. Find his gain percentage. [2014-I]
(a) 91/9 % (b) 100/9%
(c) 100/11% (d) 95/9%
44. A man purchased a bullock and a cart for ` 1800. He
sold the bullock at a profit of 20% and the cart at a profit of
30%. His total profit was 155/6 %. Find the cost price of
bullock. [2014-I]
(a) ` 650 (b) ` 750
(c) ` 900 (d) ` 800
45. If a person repaid ` 22500 after 10 years of borrowing a loan,
at 10% per annum simple interest find out what amount did
he take as a loan ? [2014-I]
(a) 11,225 (b) 11,250 (c) 10,000 (d) 7,500
46. A sum of money invested at simple interest triples itself
in 8 years. How many times will it become in 20 years
time ?      [2014-I]
(a) 8 times (b) 7 times (c) 6 times (d)   9 times
47. Two-third of a consignment was sold at a profit of 5% and
the remainder at a loss of 2% if the total profit was `400,
what was the value of the consignment ? [2014-II]
(a) `13,000/- (b) `17,000/-
(c) `15,000/- (d) `40,000/-
48. In three annual examinations' of which the aggregate marks
of each was 500, a student secured average marks 45% and
55% in the first and the second yearly examinations
respectively. To secure 60% average total marks, it is
necessary for him in third yearly examination to secure
___ marks. [2014-II]
(a) 3 00 (b) 3 50
(c) 3 55 (d) 4 00
49. A towel was 50 cm broad and 100 cm long. When bleached, it
was found to have lost 20% of its length and 10% of its
breadth. Find the percentage of decrease in area ?[2014-II]
(a) 32% (b) 28%
(c) 33% (d) 24%
50. A man deposited a total sum of ` 88400/- in the name of his
two sons aged 19 and 17 years so that at the age of 21, both
will get equal amounts. If the money is invested at the rate
of 10% compound interest per annum what are the shares of
his two sons ? [2014-II]
(a) `48200/- (b) `48400
(c) `42600/- (d) `44200
51. The sum of the number of boys and girls in a school is 150.
If the number of boys is x, then the number of girls becomes
x% of the total number of students. How many boys are
there in the school ? [2014-II]
(a) 51 (b) 65
(c) 60 (d) 95
52. 'A' scored 30% marks and failed by 15 marks. 'B' scored 40%
marks and obtained 35 marks more than those required to
pass what is the pass percentage ? [2014-II]
(a) 33% (b) 40%
(c) 34% (d) 48%
53. A banker lent `6000/- at 10% and `5000/- at 12% at the same
time and for same period of time. The banker received `2400
as total interest on both loans. Find the period for which the
banker had lent the amount. [2014-II]
(a) 3 years 6 months (b) 3 years
(c) 2 years 6 months (d) 2 years
54. If  a sum becomes double in 16 years, how many times will it
be in 8 years? [2015-I]
(a)
1
1
2
 times (b)
1
1
3
 times
(c)
3
1
4
 items (d)
1
1
4
 times
55. In how many years will a sum of ` 800 at 10% per annum
compounded semi-annually become ` 926.10? [2015-I]
(a)
1
1
3
(b)
1
1
2
(c)
1
2
3
(d)
1
2
2
56. A sell 2 TV sets, one at a loss of 15% and another at a  profit
of 15%. Find the loss/gain percentage in the overall
transaction? [2015-I]
(a) 2.25% (b) 3%
(c) 4% (d) No profit, no loss
57. The price of sugar increases by 20% due to the festive
season. by what percentage should a family reduce the
consumption of sugar so that there is no change in the
expenditure ? [2015-I]
(a) 20% (b)
1
18%
3
(c)
2
16%
3
(d)    
1
16%
3
58. A's salary is 20% lower than B's salary , which is 15% lower
than C's salary. By how much percent is C's salary more
than A's salary? [2015-I]
(a) 44.05% (b) 45.05%
(c) 46.05% (d) 47.05%
59. If 2x – 
1
6,
2x
= then the value of 
2
2
1
x
16x
+
 is   [2018 - I]
(a)
19
2
(b)
17
2
(c)
18
3
(d)
15
2
60. x
4
 + 4 is equal to: [2019 - II]
(a) (x
2
 + 2) (x
2
 – 2) (b) (x
2
 + 2x + 2) (x
2
 – 2x + 2)
(c) (x
2
 + 2)
2
(d) (x – 1) (x + 1) (x + 2) (x – 2)
61. If A - B = 3 and A
2
 + B
2
 = 29, find the value of AB. [2020 - I]
( a) 10 (b) 1 2 (c ) 15 (d) 1 8
62. If 
2
51
3
2 51
x
xx
=
++
, then the value of 
1
2
x
x
æö
+
ç÷
èø
is
(a) 15 (b) 10 (c) 20 (d) 5
Page 4


B-30 Algebra
Algebra
3
1. In an examination a candidate has to get 35% of total marks
to pass. In one paper he gets 62 out of 150 and in the second
35 out of 150. How many marks should he get out of 200
marks in the third paper to pass ? [2011-I]
(a) 61 (b) 68
(c) 70 (d) 78
2. The salary of A & B together amounts to ` 2000. A spends
95% of his salary and B 85% of his salary . If their savings
are same what is the salary of A ? [2011-I]
(a) ` 750 (b) ` 1250
(c) ` 1500 (d) ` 1600
3. Out of the 1000 inhabitants of a town, 60% are male of whom
20% are literate. If, amongst all the inhabitants, 25% are
literate, then what percentage of the females of the town are
literate ? [2011-I]
(a) 2 2.5 (b) 32.5
(c) 27.5 (d) 37.5
4. A trader mixes 26 kg of rice at ` 20 per kg with 30 kg rice of
another variety costing ` 36 per kg. If he sells the mixture at
` 30 per kg his profit will be- [2011-I]
(a) –7% (b) 5%
(c) 8% (d) 10%
5. The difference between the cost price and sale price is `
240. If the profit is 20%, the selling price is [2011-I]
(a) ` 1200 (b) ` 1440
(c) ` 1800 (d) ` 2440
6. Samant bought a microwave oven and paid 10% less than
Maximum Retail Price(MRP). He sold it with 30% profit
on his purchase cost. What percentage of profit did he earn on
MRP ? [2011-I]
(a) 17% (b) 20%
(c) 27% (d) 32%
7. ` 800 becomes ` 956 in 3 years at a certain rate of interest.
If the rate of interest is increased by 4% what amount will
` 800 become in 3 years ? [2011-I]
(a) ` 1020 (b) ` 1052
(c) ` 1282 (d) ` 1080
8. How much time will it take for an amount of ` 450 to gain
` 81 as interest, if rate of interest is 4.5% p.a on simple
interest ? [2011-I]
(a) 4.5 years (b) 3.5 years
(c) 5 years (d) 4 years
9. At what rate of annual simple interest will `10000 double in
15 years ? [2011-I]
(a) 5.5% (b) 8%
(c) 6.67% (d) 7.25%
10. What percentage of profit should be added in the cost price
of an item so as to gain a profit of 33% after allowing 5%
discount to the customer ? [2011-II]
(a) 45 (b) 40
(c) 52 (d) 48
11. If the manufacturer gains 10%, the wholesale dealer gains
15% and the retailer gains 25%, find the cost of production
of a table. The retail price of table is ` 1265 [2011-II]
(a) ` 800 (b) ` 1000
(c) ` 950 (d) ` 1180
12. A loss of 19% on a shirt gets converted into a profit of 17%
when the selling price is increased by ` 162. What is the
cost price of the shirt ? [2011-II]
(a) ` 540 (b) ` 450
(c) ` 600 (d) ` 360
13. In an examination 75% of the total students passed in English
and 65% passed in Mathematics, while 15% failed in English
as well as Mathematics. If a total of 495 candidates who
passed in both exams. Find the total number of students
who appeared in the exam. [2011-II]
(a) 8 50 (b) 9 00
(c) 1000 (d) 1050
14. When the price of a product was increased by 15%, the
number of items sold was decreased by 20%. What was the net
effect ? [2011-II]
(a) 10% gain (b) 6% loss
(c) 8% loss (d) 4% gain
15. A mixture of 40 litres of milk and water contains 10% water.
How much water should be added to this mixture so that the
new mixture contains 20% water ? [2011-II]
(a) 4 litres (b) 5 litres
(c) 6.5 litres (d) 7.5 litres
16. A certain sum of money becomes three times of itself
in 20 years at simple interest. In how many years will
the initial sum become double at the same rate of simple
interest ? [2011-II]
(a)8 (b) 10
(c) 12 (d) 14
17. Ram borrows ` 8000 at 12% p.a. simple interest and Mohan
borrows ` 9100 at 10% p.a. simple interest. In how many years
will their borrowed amounts (debt) be equal ? [2011-II]
(a) 18 (b) 2 0
(c) 22 (d) 2 4
Algebra
18. Reena took a loan of ` 1200 with simple interest for a certain
numbers of years. The number years are same as the interest
rate. If she has paid ` 432 as interest at the end of the loan
period, what was the rate of interest ? [2011-II]
(a) 3.6 (b) 6
(c) 12 (d) None of these
19. Hari’s income is 20% more than Madhu’s income. Madhu’s
income is less than Hari’s income by [2012-I]
(a) 15% (b) 16.66 %
(c) 2 0% (d) 22.25%
20. A sum of money lent out at simple interest doubled itself in
20 years. In how many years will it triple itself ? [2012-I]
(a) 28 yrs (b) 30 yrs
(c) 40 yrs (d) 35 yrs
21. One litre of water is evaporated from 6 litres of a solution
containing 5% salt. The percentage of salt in the remaining
solution is [2012-I]
(a) 16% (b) 5%
(c) 4% (d) 6%
22. A shopkeeper professes to sell all things at a discount of
10% but increases the selling price of each article by 20%.
His gain on each article is [2012-I]
(a) 6% (b) 8%
(c) 1 0% (d) 12%
23. If the selling price of an article is 4/3
rd
 of its cost price, the
profit in transaction is [2012-I]
(a) 16.75% (b) 20.50%
(c) 25.50% (d) 33.33%
24. If selling price is doubled, the profit triples. Find the profit
percent. [2012-I]
(a) 66.66 (b) 1 00
(c) 105.33 (d) 1 20
25. Srinivasan invests two equal amounts in two banks giving
10% and 12% rate of interest respectively. At the end of
year the interest earned is ` 1650. Find the sum invested in
each. [2012-II]
(a) `  8500 (b) `  15000
(c) `  7500 (d) `  17,000
26. The simple interest on sum of money is 1/9 of the sum. The
number of years is numerically equal to the rate percent per
annum. The rate percent per annum is [2012-II]
(a) 3.33 (b) 5
(c) 6.66 (d) 10
27. A sum of ` 10.000 is lent partly at 8% and the remaining at
10% per annum, If the yearly  interest on the average is
9.2%. the money lent at 10% is [2012-II]
(a) `  6000 (b) `  5500
(c) `  5000 (d) `  4500
28. In an election between two candidates, 60% of the voters
cast their votes, out of which 4% of the votes were declared
invalid. A candidate got 7344 votes which were 75% of the
total valid votes. Find the total number of votes enrolled in
that election. [2012-II]
(a) 1700 (b) 17590
(c) 17000 (d) 7344
29. If the price of kerosene be raised by 9%, find how much
percent a house holder must reduce his consumption of
kerosene so that not to increase his expenditure [2012-II]
(a) 9% (b) 8.25%
(c) 9% (d) 9.25%
30. Sixty five pupils from a school entered for an examination
and 80% of them passed. Another school entered 10 more
pupils than the first school and four more pupils passed.
The % of pass in the second school was [2012-II]
(a) 75% (b) 84%
(c) 72% (d) 74.6%
31. Calculate the amount on ` 1250 for 2 years at 4% per annum.
compounded yearly. [2012-II]
(a) ` 676 (b) ` 1352
(c) ` 1778 (d) ` 255
32. A sum of ` 3200 is lent out into two parts, one at 6% and
another at 4%. If the total annual income is ` 176, find the
money lent at 6%. [2012-II]
(a) `  2400 (b) ` 800
(c) `  1600 (d) ` 3200
33. Srinivasan invests two equal amounts in two banks
giving 8% and 12% rate of interest respectively. At the end
of year the interest earned is ` 1500. Find the sum invested
in each. [2013-I]
(a) ` 8500 (b) ` 15000
(c) ` 7500 (d) ` 17000
34. The simple interest accrued on a sum of money at the end of
four years is 1/5
th
 of its principal. What is the rate of interest
per annum ? [2013-I]
(a) 4% (b) 5%
(c) 6% (d) Inadequate data
35. A sum of ` 2600 is lent out into two parts, one at 9% and
another at 7%. If the total annual income is ` 206, find the
money lent at 7%. [2013-I]
(a) ` 1400 (b) ` 900
(c) ` 1600 (d) ` 1200
36. In an election between two candidates, 70% of the voters
cast their votes, out of which 2% of the votes were declared
invalid. A candidate got 7203 votes which was 60% of the
total valid votes. Find the total number of voters enrolled in
that election. [2013-I]
(a) 18050 (b) 17500
(c) 17000 (d) 7203
37. If the price of kerosene be raised by 11%, find by how much
percent a house holder must reduce his consumption of
kerosene so as not to increase his expenditure ? [2013-I]
(a) 1 1% (b) 9.9%
(c) 11.09% (c) 8.25%
38. 75 pupils from a school appeared for an examination and
80% of them passed. Another school entered 10 more pupils
than the first school and five pupils less than the first school
passed. The pass % of in the second school was [2013-I]
(a) 75% (b) 84%
(c) 72% (d) 64.7%
39. Calculate the amount on ` 1875 for 2 years at 4% per annum,
compounded yearly. [2013-I]
(a) ` 676 (b) ` 776
(c) ` 1778 (d) ` 2028
40. If x varies as y and x = 8 when y = 15 then the values of x
when y = 10 is [2013-I]
(a)5 (b) 15/8
(c) 8/15 (d) 16/3
Algebra
41. A sum of ` 10,000 is lent partly at 6% and the remaining at
10% p.a. If the yearly interest on the average is 9.2%, the
money lent at 10% is [2013-I]
(a) ` 2000 (b) ` 8500
(c) ` 5000 (d) ` 8000
42. An article costs ` 50 presently . The rate of inflation is 300%.
What will be cost of this article after two years ? [2014-I]
(a) ` 200 (b) ` 600
(c) ` 800 (d) ` 1000
43. A dishonest shopkeeper professes to sell his groceries at
his cost price, but uses a false weight of 900 grams for each
kilogram. Find his gain percentage. [2014-I]
(a) 91/9 % (b) 100/9%
(c) 100/11% (d) 95/9%
44. A man purchased a bullock and a cart for ` 1800. He
sold the bullock at a profit of 20% and the cart at a profit of
30%. His total profit was 155/6 %. Find the cost price of
bullock. [2014-I]
(a) ` 650 (b) ` 750
(c) ` 900 (d) ` 800
45. If a person repaid ` 22500 after 10 years of borrowing a loan,
at 10% per annum simple interest find out what amount did
he take as a loan ? [2014-I]
(a) 11,225 (b) 11,250 (c) 10,000 (d) 7,500
46. A sum of money invested at simple interest triples itself
in 8 years. How many times will it become in 20 years
time ?      [2014-I]
(a) 8 times (b) 7 times (c) 6 times (d)   9 times
47. Two-third of a consignment was sold at a profit of 5% and
the remainder at a loss of 2% if the total profit was `400,
what was the value of the consignment ? [2014-II]
(a) `13,000/- (b) `17,000/-
(c) `15,000/- (d) `40,000/-
48. In three annual examinations' of which the aggregate marks
of each was 500, a student secured average marks 45% and
55% in the first and the second yearly examinations
respectively. To secure 60% average total marks, it is
necessary for him in third yearly examination to secure
___ marks. [2014-II]
(a) 3 00 (b) 3 50
(c) 3 55 (d) 4 00
49. A towel was 50 cm broad and 100 cm long. When bleached, it
was found to have lost 20% of its length and 10% of its
breadth. Find the percentage of decrease in area ?[2014-II]
(a) 32% (b) 28%
(c) 33% (d) 24%
50. A man deposited a total sum of ` 88400/- in the name of his
two sons aged 19 and 17 years so that at the age of 21, both
will get equal amounts. If the money is invested at the rate
of 10% compound interest per annum what are the shares of
his two sons ? [2014-II]
(a) `48200/- (b) `48400
(c) `42600/- (d) `44200
51. The sum of the number of boys and girls in a school is 150.
If the number of boys is x, then the number of girls becomes
x% of the total number of students. How many boys are
there in the school ? [2014-II]
(a) 51 (b) 65
(c) 60 (d) 95
52. 'A' scored 30% marks and failed by 15 marks. 'B' scored 40%
marks and obtained 35 marks more than those required to
pass what is the pass percentage ? [2014-II]
(a) 33% (b) 40%
(c) 34% (d) 48%
53. A banker lent `6000/- at 10% and `5000/- at 12% at the same
time and for same period of time. The banker received `2400
as total interest on both loans. Find the period for which the
banker had lent the amount. [2014-II]
(a) 3 years 6 months (b) 3 years
(c) 2 years 6 months (d) 2 years
54. If  a sum becomes double in 16 years, how many times will it
be in 8 years? [2015-I]
(a)
1
1
2
 times (b)
1
1
3
 times
(c)
3
1
4
 items (d)
1
1
4
 times
55. In how many years will a sum of ` 800 at 10% per annum
compounded semi-annually become ` 926.10? [2015-I]
(a)
1
1
3
(b)
1
1
2
(c)
1
2
3
(d)
1
2
2
56. A sell 2 TV sets, one at a loss of 15% and another at a  profit
of 15%. Find the loss/gain percentage in the overall
transaction? [2015-I]
(a) 2.25% (b) 3%
(c) 4% (d) No profit, no loss
57. The price of sugar increases by 20% due to the festive
season. by what percentage should a family reduce the
consumption of sugar so that there is no change in the
expenditure ? [2015-I]
(a) 20% (b)
1
18%
3
(c)
2
16%
3
(d)    
1
16%
3
58. A's salary is 20% lower than B's salary , which is 15% lower
than C's salary. By how much percent is C's salary more
than A's salary? [2015-I]
(a) 44.05% (b) 45.05%
(c) 46.05% (d) 47.05%
59. If 2x – 
1
6,
2x
= then the value of 
2
2
1
x
16x
+
 is   [2018 - I]
(a)
19
2
(b)
17
2
(c)
18
3
(d)
15
2
60. x
4
 + 4 is equal to: [2019 - II]
(a) (x
2
 + 2) (x
2
 – 2) (b) (x
2
 + 2x + 2) (x
2
 – 2x + 2)
(c) (x
2
 + 2)
2
(d) (x – 1) (x + 1) (x + 2) (x – 2)
61. If A - B = 3 and A
2
 + B
2
 = 29, find the value of AB. [2020 - I]
( a) 10 (b) 1 2 (c ) 15 (d) 1 8
62. If 
2
51
3
2 51
x
xx
=
++
, then the value of 
1
2
x
x
æö
+
ç÷
èø
is
(a) 15 (b) 10 (c) 20 (d) 5
Algebra
ANSWERS & EXPLANATIONS
1. (d) Total marks = 150 + 150 + 200 = 500
35%  of  500 = 175
175 = 62 + 35 + x
x = 78
2. (c) Let the salary of A and B are x and (2000 – x) resp.
According to question
x – 95% of x = [(2000 – x – 85% of (2000 – x)]
( )
95 85
x1 2000x1
100 100
éù éù
- = --
êú êú
ëû ëû
5x = (2000 – x) 15
20x = 30000
x = 1500
Hence, the salary of A is ` 1500.
3. (b) Total number of males those are literate = 60% of 20%
of 1000
=
60 20
1000
100 100
´´
= 120
Total number of males in the town = 600
Total number of females in the town = 400
Total number of all inhabitants those are literate = 25%
of 1000 = 250
Remaining females those are literates = 250 – 120 = 130
\ Required % = 
130
100
400
´
  =  32.5%
4. (b) C. P. of 56 kg rice
= (26 × 20 + 30 × 36) = ` (520 + 1080) = ` 1600
S. P. of 56 kg rice = 56 × 30 = ` 1680
Profit % = 
80
100 5%
1600
´=
5. (b) Profit = S. P – C. P
Profit = 240
Profit % = 
Profit
100
C.P.
´
240
20 100 C.P. 1200
C.P.
= ´ Þ=
Therefore, S.P = 1200 + 240 = ` 1440
6. (a) Let the original price = `100
Then, C.P. = ` 90
S. P. = 130% of 90 = ` 
130
90
100
æö
´
ç÷
èø
 =  ` 117
\ Required percentage = (117 – 100)
= 17%
7. (b) S.I. = ` (956 – 800) = ` 156;
P = 800, T = 3 yrs.
Q
100 156
R % 6.5%
8003
´ æö
==
ç÷
´
èø
New rate = (6.5 + 4) = 10.5%
New, S.I = ` 
800 10.5 3
100
´´ æö
ç÷
èø
= ` 252
\ New amount = 800 + 252 = 1052
8. (d) SI = 
PRT
100
´´
81 = 
450 4.5 T
100
´´
100 81
T 4 years
450 4.5
´
==
´
9. (c) S.I = 2P – P = P
P = 
P × R ×15
100
R = 
100
6.67%
15
=
10. (b) Let the C.P = ` 100
The, S.P = `133
Let the marked price ` x
Then, 95% of x = 133
x = 
133 100
140
95
´
=
Marked price = 40% above C.P.
11. (a) Let the cost of production of a table = ` x.
110 115 125
x 1265
100 100 100
´ ´ ´=
1265 1000000
x
110 115 125
´
=
´´
= ` 800
12. (b) Let C. P. = x
Loss = 19%
then S.P. is 
100 –19 81
xx
100 100
æö
=
ç÷
èø
If profit = 17% then S. P. = 
100 17 117
xx
100 100
+ æö
=
ç÷
èø
According to question
81 117
x 162 x
100 100
+=
\ x = 450
13. (b) Let A and B represent the sets of students who passed
in English and Mathematics respectively.
If 15% of candidates failed in both, then 85% passed at
least one of the exams.
Then, the total number of students passed in one or
both subjects
=n( ) ( ) ( ) ( ) A B nA nB nA B È = + =Ç
0.85= 0.75 +0.65 – ( ) nAB Ç
Page 5


B-30 Algebra
Algebra
3
1. In an examination a candidate has to get 35% of total marks
to pass. In one paper he gets 62 out of 150 and in the second
35 out of 150. How many marks should he get out of 200
marks in the third paper to pass ? [2011-I]
(a) 61 (b) 68
(c) 70 (d) 78
2. The salary of A & B together amounts to ` 2000. A spends
95% of his salary and B 85% of his salary . If their savings
are same what is the salary of A ? [2011-I]
(a) ` 750 (b) ` 1250
(c) ` 1500 (d) ` 1600
3. Out of the 1000 inhabitants of a town, 60% are male of whom
20% are literate. If, amongst all the inhabitants, 25% are
literate, then what percentage of the females of the town are
literate ? [2011-I]
(a) 2 2.5 (b) 32.5
(c) 27.5 (d) 37.5
4. A trader mixes 26 kg of rice at ` 20 per kg with 30 kg rice of
another variety costing ` 36 per kg. If he sells the mixture at
` 30 per kg his profit will be- [2011-I]
(a) –7% (b) 5%
(c) 8% (d) 10%
5. The difference between the cost price and sale price is `
240. If the profit is 20%, the selling price is [2011-I]
(a) ` 1200 (b) ` 1440
(c) ` 1800 (d) ` 2440
6. Samant bought a microwave oven and paid 10% less than
Maximum Retail Price(MRP). He sold it with 30% profit
on his purchase cost. What percentage of profit did he earn on
MRP ? [2011-I]
(a) 17% (b) 20%
(c) 27% (d) 32%
7. ` 800 becomes ` 956 in 3 years at a certain rate of interest.
If the rate of interest is increased by 4% what amount will
` 800 become in 3 years ? [2011-I]
(a) ` 1020 (b) ` 1052
(c) ` 1282 (d) ` 1080
8. How much time will it take for an amount of ` 450 to gain
` 81 as interest, if rate of interest is 4.5% p.a on simple
interest ? [2011-I]
(a) 4.5 years (b) 3.5 years
(c) 5 years (d) 4 years
9. At what rate of annual simple interest will `10000 double in
15 years ? [2011-I]
(a) 5.5% (b) 8%
(c) 6.67% (d) 7.25%
10. What percentage of profit should be added in the cost price
of an item so as to gain a profit of 33% after allowing 5%
discount to the customer ? [2011-II]
(a) 45 (b) 40
(c) 52 (d) 48
11. If the manufacturer gains 10%, the wholesale dealer gains
15% and the retailer gains 25%, find the cost of production
of a table. The retail price of table is ` 1265 [2011-II]
(a) ` 800 (b) ` 1000
(c) ` 950 (d) ` 1180
12. A loss of 19% on a shirt gets converted into a profit of 17%
when the selling price is increased by ` 162. What is the
cost price of the shirt ? [2011-II]
(a) ` 540 (b) ` 450
(c) ` 600 (d) ` 360
13. In an examination 75% of the total students passed in English
and 65% passed in Mathematics, while 15% failed in English
as well as Mathematics. If a total of 495 candidates who
passed in both exams. Find the total number of students
who appeared in the exam. [2011-II]
(a) 8 50 (b) 9 00
(c) 1000 (d) 1050
14. When the price of a product was increased by 15%, the
number of items sold was decreased by 20%. What was the net
effect ? [2011-II]
(a) 10% gain (b) 6% loss
(c) 8% loss (d) 4% gain
15. A mixture of 40 litres of milk and water contains 10% water.
How much water should be added to this mixture so that the
new mixture contains 20% water ? [2011-II]
(a) 4 litres (b) 5 litres
(c) 6.5 litres (d) 7.5 litres
16. A certain sum of money becomes three times of itself
in 20 years at simple interest. In how many years will
the initial sum become double at the same rate of simple
interest ? [2011-II]
(a)8 (b) 10
(c) 12 (d) 14
17. Ram borrows ` 8000 at 12% p.a. simple interest and Mohan
borrows ` 9100 at 10% p.a. simple interest. In how many years
will their borrowed amounts (debt) be equal ? [2011-II]
(a) 18 (b) 2 0
(c) 22 (d) 2 4
Algebra
18. Reena took a loan of ` 1200 with simple interest for a certain
numbers of years. The number years are same as the interest
rate. If she has paid ` 432 as interest at the end of the loan
period, what was the rate of interest ? [2011-II]
(a) 3.6 (b) 6
(c) 12 (d) None of these
19. Hari’s income is 20% more than Madhu’s income. Madhu’s
income is less than Hari’s income by [2012-I]
(a) 15% (b) 16.66 %
(c) 2 0% (d) 22.25%
20. A sum of money lent out at simple interest doubled itself in
20 years. In how many years will it triple itself ? [2012-I]
(a) 28 yrs (b) 30 yrs
(c) 40 yrs (d) 35 yrs
21. One litre of water is evaporated from 6 litres of a solution
containing 5% salt. The percentage of salt in the remaining
solution is [2012-I]
(a) 16% (b) 5%
(c) 4% (d) 6%
22. A shopkeeper professes to sell all things at a discount of
10% but increases the selling price of each article by 20%.
His gain on each article is [2012-I]
(a) 6% (b) 8%
(c) 1 0% (d) 12%
23. If the selling price of an article is 4/3
rd
 of its cost price, the
profit in transaction is [2012-I]
(a) 16.75% (b) 20.50%
(c) 25.50% (d) 33.33%
24. If selling price is doubled, the profit triples. Find the profit
percent. [2012-I]
(a) 66.66 (b) 1 00
(c) 105.33 (d) 1 20
25. Srinivasan invests two equal amounts in two banks giving
10% and 12% rate of interest respectively. At the end of
year the interest earned is ` 1650. Find the sum invested in
each. [2012-II]
(a) `  8500 (b) `  15000
(c) `  7500 (d) `  17,000
26. The simple interest on sum of money is 1/9 of the sum. The
number of years is numerically equal to the rate percent per
annum. The rate percent per annum is [2012-II]
(a) 3.33 (b) 5
(c) 6.66 (d) 10
27. A sum of ` 10.000 is lent partly at 8% and the remaining at
10% per annum, If the yearly  interest on the average is
9.2%. the money lent at 10% is [2012-II]
(a) `  6000 (b) `  5500
(c) `  5000 (d) `  4500
28. In an election between two candidates, 60% of the voters
cast their votes, out of which 4% of the votes were declared
invalid. A candidate got 7344 votes which were 75% of the
total valid votes. Find the total number of votes enrolled in
that election. [2012-II]
(a) 1700 (b) 17590
(c) 17000 (d) 7344
29. If the price of kerosene be raised by 9%, find how much
percent a house holder must reduce his consumption of
kerosene so that not to increase his expenditure [2012-II]
(a) 9% (b) 8.25%
(c) 9% (d) 9.25%
30. Sixty five pupils from a school entered for an examination
and 80% of them passed. Another school entered 10 more
pupils than the first school and four more pupils passed.
The % of pass in the second school was [2012-II]
(a) 75% (b) 84%
(c) 72% (d) 74.6%
31. Calculate the amount on ` 1250 for 2 years at 4% per annum.
compounded yearly. [2012-II]
(a) ` 676 (b) ` 1352
(c) ` 1778 (d) ` 255
32. A sum of ` 3200 is lent out into two parts, one at 6% and
another at 4%. If the total annual income is ` 176, find the
money lent at 6%. [2012-II]
(a) `  2400 (b) ` 800
(c) `  1600 (d) ` 3200
33. Srinivasan invests two equal amounts in two banks
giving 8% and 12% rate of interest respectively. At the end
of year the interest earned is ` 1500. Find the sum invested
in each. [2013-I]
(a) ` 8500 (b) ` 15000
(c) ` 7500 (d) ` 17000
34. The simple interest accrued on a sum of money at the end of
four years is 1/5
th
 of its principal. What is the rate of interest
per annum ? [2013-I]
(a) 4% (b) 5%
(c) 6% (d) Inadequate data
35. A sum of ` 2600 is lent out into two parts, one at 9% and
another at 7%. If the total annual income is ` 206, find the
money lent at 7%. [2013-I]
(a) ` 1400 (b) ` 900
(c) ` 1600 (d) ` 1200
36. In an election between two candidates, 70% of the voters
cast their votes, out of which 2% of the votes were declared
invalid. A candidate got 7203 votes which was 60% of the
total valid votes. Find the total number of voters enrolled in
that election. [2013-I]
(a) 18050 (b) 17500
(c) 17000 (d) 7203
37. If the price of kerosene be raised by 11%, find by how much
percent a house holder must reduce his consumption of
kerosene so as not to increase his expenditure ? [2013-I]
(a) 1 1% (b) 9.9%
(c) 11.09% (c) 8.25%
38. 75 pupils from a school appeared for an examination and
80% of them passed. Another school entered 10 more pupils
than the first school and five pupils less than the first school
passed. The pass % of in the second school was [2013-I]
(a) 75% (b) 84%
(c) 72% (d) 64.7%
39. Calculate the amount on ` 1875 for 2 years at 4% per annum,
compounded yearly. [2013-I]
(a) ` 676 (b) ` 776
(c) ` 1778 (d) ` 2028
40. If x varies as y and x = 8 when y = 15 then the values of x
when y = 10 is [2013-I]
(a)5 (b) 15/8
(c) 8/15 (d) 16/3
Algebra
41. A sum of ` 10,000 is lent partly at 6% and the remaining at
10% p.a. If the yearly interest on the average is 9.2%, the
money lent at 10% is [2013-I]
(a) ` 2000 (b) ` 8500
(c) ` 5000 (d) ` 8000
42. An article costs ` 50 presently . The rate of inflation is 300%.
What will be cost of this article after two years ? [2014-I]
(a) ` 200 (b) ` 600
(c) ` 800 (d) ` 1000
43. A dishonest shopkeeper professes to sell his groceries at
his cost price, but uses a false weight of 900 grams for each
kilogram. Find his gain percentage. [2014-I]
(a) 91/9 % (b) 100/9%
(c) 100/11% (d) 95/9%
44. A man purchased a bullock and a cart for ` 1800. He
sold the bullock at a profit of 20% and the cart at a profit of
30%. His total profit was 155/6 %. Find the cost price of
bullock. [2014-I]
(a) ` 650 (b) ` 750
(c) ` 900 (d) ` 800
45. If a person repaid ` 22500 after 10 years of borrowing a loan,
at 10% per annum simple interest find out what amount did
he take as a loan ? [2014-I]
(a) 11,225 (b) 11,250 (c) 10,000 (d) 7,500
46. A sum of money invested at simple interest triples itself
in 8 years. How many times will it become in 20 years
time ?      [2014-I]
(a) 8 times (b) 7 times (c) 6 times (d)   9 times
47. Two-third of a consignment was sold at a profit of 5% and
the remainder at a loss of 2% if the total profit was `400,
what was the value of the consignment ? [2014-II]
(a) `13,000/- (b) `17,000/-
(c) `15,000/- (d) `40,000/-
48. In three annual examinations' of which the aggregate marks
of each was 500, a student secured average marks 45% and
55% in the first and the second yearly examinations
respectively. To secure 60% average total marks, it is
necessary for him in third yearly examination to secure
___ marks. [2014-II]
(a) 3 00 (b) 3 50
(c) 3 55 (d) 4 00
49. A towel was 50 cm broad and 100 cm long. When bleached, it
was found to have lost 20% of its length and 10% of its
breadth. Find the percentage of decrease in area ?[2014-II]
(a) 32% (b) 28%
(c) 33% (d) 24%
50. A man deposited a total sum of ` 88400/- in the name of his
two sons aged 19 and 17 years so that at the age of 21, both
will get equal amounts. If the money is invested at the rate
of 10% compound interest per annum what are the shares of
his two sons ? [2014-II]
(a) `48200/- (b) `48400
(c) `42600/- (d) `44200
51. The sum of the number of boys and girls in a school is 150.
If the number of boys is x, then the number of girls becomes
x% of the total number of students. How many boys are
there in the school ? [2014-II]
(a) 51 (b) 65
(c) 60 (d) 95
52. 'A' scored 30% marks and failed by 15 marks. 'B' scored 40%
marks and obtained 35 marks more than those required to
pass what is the pass percentage ? [2014-II]
(a) 33% (b) 40%
(c) 34% (d) 48%
53. A banker lent `6000/- at 10% and `5000/- at 12% at the same
time and for same period of time. The banker received `2400
as total interest on both loans. Find the period for which the
banker had lent the amount. [2014-II]
(a) 3 years 6 months (b) 3 years
(c) 2 years 6 months (d) 2 years
54. If  a sum becomes double in 16 years, how many times will it
be in 8 years? [2015-I]
(a)
1
1
2
 times (b)
1
1
3
 times
(c)
3
1
4
 items (d)
1
1
4
 times
55. In how many years will a sum of ` 800 at 10% per annum
compounded semi-annually become ` 926.10? [2015-I]
(a)
1
1
3
(b)
1
1
2
(c)
1
2
3
(d)
1
2
2
56. A sell 2 TV sets, one at a loss of 15% and another at a  profit
of 15%. Find the loss/gain percentage in the overall
transaction? [2015-I]
(a) 2.25% (b) 3%
(c) 4% (d) No profit, no loss
57. The price of sugar increases by 20% due to the festive
season. by what percentage should a family reduce the
consumption of sugar so that there is no change in the
expenditure ? [2015-I]
(a) 20% (b)
1
18%
3
(c)
2
16%
3
(d)    
1
16%
3
58. A's salary is 20% lower than B's salary , which is 15% lower
than C's salary. By how much percent is C's salary more
than A's salary? [2015-I]
(a) 44.05% (b) 45.05%
(c) 46.05% (d) 47.05%
59. If 2x – 
1
6,
2x
= then the value of 
2
2
1
x
16x
+
 is   [2018 - I]
(a)
19
2
(b)
17
2
(c)
18
3
(d)
15
2
60. x
4
 + 4 is equal to: [2019 - II]
(a) (x
2
 + 2) (x
2
 – 2) (b) (x
2
 + 2x + 2) (x
2
 – 2x + 2)
(c) (x
2
 + 2)
2
(d) (x – 1) (x + 1) (x + 2) (x – 2)
61. If A - B = 3 and A
2
 + B
2
 = 29, find the value of AB. [2020 - I]
( a) 10 (b) 1 2 (c ) 15 (d) 1 8
62. If 
2
51
3
2 51
x
xx
=
++
, then the value of 
1
2
x
x
æö
+
ç÷
èø
is
(a) 15 (b) 10 (c) 20 (d) 5
Algebra
ANSWERS & EXPLANATIONS
1. (d) Total marks = 150 + 150 + 200 = 500
35%  of  500 = 175
175 = 62 + 35 + x
x = 78
2. (c) Let the salary of A and B are x and (2000 – x) resp.
According to question
x – 95% of x = [(2000 – x – 85% of (2000 – x)]
( )
95 85
x1 2000x1
100 100
éù éù
- = --
êú êú
ëû ëû
5x = (2000 – x) 15
20x = 30000
x = 1500
Hence, the salary of A is ` 1500.
3. (b) Total number of males those are literate = 60% of 20%
of 1000
=
60 20
1000
100 100
´´
= 120
Total number of males in the town = 600
Total number of females in the town = 400
Total number of all inhabitants those are literate = 25%
of 1000 = 250
Remaining females those are literates = 250 – 120 = 130
\ Required % = 
130
100
400
´
  =  32.5%
4. (b) C. P. of 56 kg rice
= (26 × 20 + 30 × 36) = ` (520 + 1080) = ` 1600
S. P. of 56 kg rice = 56 × 30 = ` 1680
Profit % = 
80
100 5%
1600
´=
5. (b) Profit = S. P – C. P
Profit = 240
Profit % = 
Profit
100
C.P.
´
240
20 100 C.P. 1200
C.P.
= ´ Þ=
Therefore, S.P = 1200 + 240 = ` 1440
6. (a) Let the original price = `100
Then, C.P. = ` 90
S. P. = 130% of 90 = ` 
130
90
100
æö
´
ç÷
èø
 =  ` 117
\ Required percentage = (117 – 100)
= 17%
7. (b) S.I. = ` (956 – 800) = ` 156;
P = 800, T = 3 yrs.
Q
100 156
R % 6.5%
8003
´ æö
==
ç÷
´
èø
New rate = (6.5 + 4) = 10.5%
New, S.I = ` 
800 10.5 3
100
´´ æö
ç÷
èø
= ` 252
\ New amount = 800 + 252 = 1052
8. (d) SI = 
PRT
100
´´
81 = 
450 4.5 T
100
´´
100 81
T 4 years
450 4.5
´
==
´
9. (c) S.I = 2P – P = P
P = 
P × R ×15
100
R = 
100
6.67%
15
=
10. (b) Let the C.P = ` 100
The, S.P = `133
Let the marked price ` x
Then, 95% of x = 133
x = 
133 100
140
95
´
=
Marked price = 40% above C.P.
11. (a) Let the cost of production of a table = ` x.
110 115 125
x 1265
100 100 100
´ ´ ´=
1265 1000000
x
110 115 125
´
=
´´
= ` 800
12. (b) Let C. P. = x
Loss = 19%
then S.P. is 
100 –19 81
xx
100 100
æö
=
ç÷
èø
If profit = 17% then S. P. = 
100 17 117
xx
100 100
+ æö
=
ç÷
èø
According to question
81 117
x 162 x
100 100
+=
\ x = 450
13. (b) Let A and B represent the sets of students who passed
in English and Mathematics respectively.
If 15% of candidates failed in both, then 85% passed at
least one of the exams.
Then, the total number of students passed in one or
both subjects
=n( ) ( ) ( ) ( ) A B nA nB nA B È = + =Ç
0.85= 0.75 +0.65 – ( ) nAB Ç
Algebra
( ) nAB Ç = 1.40 – 0.85 = 0.55
0.55% of number of students = 495
\ Number of students 
495
100 900
55
= ´=
14. (c) Net effect = 
xy
xy
100
++
= 15 – 20 + 
( ) 15 20
100
´-
 = – 5 – 3 = –8
Negative sign indicates that there is a loss of 8%.
15. (b) Milk contains in mixture = 36 liters.
Water contains in mixture = 4 liters
Let ‘x’ be the water added to the mixture.
36 80
4 x 20
=
+
36 = 16 + 4x
20 = 4x
\ x = 5 litres
16. (b) Let Principal = x
Amount = 3x
Simple interest = 2x
Rate = 
2x 100
10%
x 20
´
=
´
Now, required time = 
x 100
10 years
x 10
´
=
´
17. (c) Simple interest for Ram = 
8000 12 1
960
100
´´
=
Simple interest for Mohan = 
9100101
910
100
´´
=
Let ‘x’ be the years when borrowed amount be equal.
8000 + 960 x = 9100 + 910 x
50x = 9100 – 8000
50x = 1100
x = 22 years
18. (b) Let Time = T years and Rate = T%
Then, 
1200 T R
432
100
´´
=
2
432 100
T 36
1200
´
==
T = 6
19. (b) If Hari’s income is 20% more than Madhu, then
Madhu’s income is less than Hari by
=  
20
10 % 16.66%
20 100
æö
´=
ç÷
èø
+
20. (c) Let P = x, S. I = x
Rate = 
SI 100 x 100
5%
P T x 20
´´
==
´´
Now ,  P = x,  S.I = 2x,  Rate = 5%
Time  = 
SI 100 2x 100
40 yrs
P R x5
´´
==
´´
21. (d) Amount of salt in the solution = 5% of 6 l = 0.3 l
Percentage of salt in the remaining solution 
0.3
100
5
6%
=´
=
22. (b) Let S. P . =  100%
Rate increases of 20% on S.P makes it 100% + 20%  = 120%
Later, the 10% discount make it 120% –
120
%
10
æö
ç÷
èø
= 120% – 12%
= 108%
Thus gain is 108 – 100 = 8%
23. (d) Let C. P . = ` x,  then  S.P . = ` 
4x
3
4xx
Gain = x
33
x1
Gain % 100 33.33%
3x
-=
\ ´ ´=
æö
ç÷
èø
æö
ç÷
èø
``
24. (b) Let C.P . = ` x,  S.P . = ` y
Profit =  y -  x
According to question
Profit  =  S.P . - C.P.
3 (y - x)  =  2y - x
3y - 3x =  2y - x
Þ       y =  2x
Profit =  2x - x = x
Profit % = 
x
100 % 100%
x
æö
´=
ç÷
èø
25. (c) Let ‘x’ be the sum invested in the bank.
According to question
x 101 x 121
1650
100 100
´´ ´´
+=
10x + 12x = 165000
22x = 165000
x = ` 7500
26. (a) Let sum = ` x, S.I. = 
1
x
9
Rate = R%
Time =  R yrs.
1 x RR
x
9 100
´´
=
2
100
R
9
=
R = 3.33%
27. (a)
8% 10%
0.8% 1.2%
9.2%