Number System/Simplification | IAF AFCAT Past Year Papers PDF Download

 Page 1


Number System/
Simplification
1
1. In a 225 meter long yard 26 trees are planted at equal distance,
one tree being at each end of the yard. What is the distance
between two consecutive trees ? [2011-I]
(a) 10 meters (b) 8 meters
(c) 12 meters (d) 9 meters
2. A bonus of ` 1000 is divided among three employ ees. Rohit gets
twice the amount Sachin gets. Sachin gets one fifth of what
Gagan gets. How much amount does Gagan get ? [2011-I]
(a) ` 500 (b) ` 625
(c) ` 750 (d) ` 120
3. A boy was asked to multiply a number by 25. Instead, he
multiplied the number by 52 and got the answer 324 more
than the correct answer. The number to be multiplied was
[2011-I]
( a) 12 (b) 1 5 (c) 25 (d) 3 2
4. The value of (?) in the equation 365.089 – ? + 89.72 = 302.35 is
[2011-I]
(a) 152.456 (b) 152.459
(c) 153.456 (d) 153.459
5. A sum of ` 312 is divided among 60 boys and some girls in
such a way that each boy gets ` 3.60 and each girl gets
` 2.40. The number of girls are- [2011-I]
(a) 35 (b) 6 0
(c) 40 (d) 6 5
6. The number of girls in a class in five times the number of
boys. Which of the following cannot be the total number of
children in the class ? [2011-II]
(a) 24 (b) 3 0
(c) 35 (d) 5 4
7. Ram went to a shop to buy 50 kg of rice. He bought two
varieties of rice which cost him ` 4.50 per kg and ` 5 per kg.
He spent a total of ` 240. What was the quantity of the
cheaper rice purchased by him ? [2011-II]
(a) 20 Kg (b) 25 Kg
(c) 30 Kg (d) None of these
8. A man has ` 640 in the denominations of one rupee, five
rupee and ten rupee notes. The number of each type of
notes are equal. What is the total number of notes he has ?
[2011-II]
(a) 60 (b) 1 50 (c) 90 (d) 1 20
9. A man has few hens and cows. If the total number of heads
are 48 and the total number of feet are 140, then the number
of hens are [2011-II]
(a) 22 (b) 23
(c) 24 (d) 26
10. A student was asked to divide a number by 3. But, instead
of dividing it he multiplied it by 3 and got 29.7 as the answer.
What was the correct answer had he not made the mistake ?
[2011-II]
(a) 3.3 (b) 9.3
(c) 9.8 (d) 9.9
11. Which of the following fraction is the smallest ? [2011-II]
(a) 9/13 (b) 17/26
(c) 28/39 (d) 33/52
12. Which of the following fractions are in ascending order ?
[2012-I]
(a) 2/3, 3/5,7/9,9/11,8/9 (b) 3/5, 2/3, 9/11, 7/9, 8/9
(c) 3/5, 2/3, 7/9, 9/11, 8/9 (d) 8/9, 9/11, 7/9, 2/3, 3/5
13. 337.62 + 8.591 + 34.4  = ? [2012-I]
(a) 370.611 (b) 380.511
(c) 380.611 (d) 426.97
14. Find the sum of :- 1/9+1/6+1/12+1/72 [2012-I]
(a) 3/5 (b) 3/2
(c) 3/8 (d) 4/7
15. ? % of 932 + 30 = 309.6 [2012-I]
(a) 25 (b) 3 0
(c) 35 (d) 4 0
16. The difference between a number and its two-fifth is 510.
What is 10% of that number ? [2012-I]
(a) 12.75 (b) 8 5
(c) 2 04 (d) None
17. If 4/5
th
 of an estate is worth ` 16,800, then the value of 3/7
th
of the estate is [2012-I]
(a) ` 9000 (b) ` 21000
(c) ` 72000 (d) ` 90000
18. If a/b = 3/4 and 8a + 5b=22, then the value of ‘a’ is [2012-I]
(a)1 (b) 1/2 (c) 3/2 (d) 3/4
19. If (a – b) is 6 more than (c + d) and (a + b) is 3 less than
(c – d), then the value of (a – c) is [2012-I]
(a) 0.5 (b) 1.0
(c) 1.5 (d) 2.0
20. The number whose square is equal to the difference of the
squares of 40 and 32 is [2012-II]
(a) 45.09 (b) 24
(c) 25 (d) 28
Page 2


Number System/
Simplification
1
1. In a 225 meter long yard 26 trees are planted at equal distance,
one tree being at each end of the yard. What is the distance
between two consecutive trees ? [2011-I]
(a) 10 meters (b) 8 meters
(c) 12 meters (d) 9 meters
2. A bonus of ` 1000 is divided among three employ ees. Rohit gets
twice the amount Sachin gets. Sachin gets one fifth of what
Gagan gets. How much amount does Gagan get ? [2011-I]
(a) ` 500 (b) ` 625
(c) ` 750 (d) ` 120
3. A boy was asked to multiply a number by 25. Instead, he
multiplied the number by 52 and got the answer 324 more
than the correct answer. The number to be multiplied was
[2011-I]
( a) 12 (b) 1 5 (c) 25 (d) 3 2
4. The value of (?) in the equation 365.089 – ? + 89.72 = 302.35 is
[2011-I]
(a) 152.456 (b) 152.459
(c) 153.456 (d) 153.459
5. A sum of ` 312 is divided among 60 boys and some girls in
such a way that each boy gets ` 3.60 and each girl gets
` 2.40. The number of girls are- [2011-I]
(a) 35 (b) 6 0
(c) 40 (d) 6 5
6. The number of girls in a class in five times the number of
boys. Which of the following cannot be the total number of
children in the class ? [2011-II]
(a) 24 (b) 3 0
(c) 35 (d) 5 4
7. Ram went to a shop to buy 50 kg of rice. He bought two
varieties of rice which cost him ` 4.50 per kg and ` 5 per kg.
He spent a total of ` 240. What was the quantity of the
cheaper rice purchased by him ? [2011-II]
(a) 20 Kg (b) 25 Kg
(c) 30 Kg (d) None of these
8. A man has ` 640 in the denominations of one rupee, five
rupee and ten rupee notes. The number of each type of
notes are equal. What is the total number of notes he has ?
[2011-II]
(a) 60 (b) 1 50 (c) 90 (d) 1 20
9. A man has few hens and cows. If the total number of heads
are 48 and the total number of feet are 140, then the number
of hens are [2011-II]
(a) 22 (b) 23
(c) 24 (d) 26
10. A student was asked to divide a number by 3. But, instead
of dividing it he multiplied it by 3 and got 29.7 as the answer.
What was the correct answer had he not made the mistake ?
[2011-II]
(a) 3.3 (b) 9.3
(c) 9.8 (d) 9.9
11. Which of the following fraction is the smallest ? [2011-II]
(a) 9/13 (b) 17/26
(c) 28/39 (d) 33/52
12. Which of the following fractions are in ascending order ?
[2012-I]
(a) 2/3, 3/5,7/9,9/11,8/9 (b) 3/5, 2/3, 9/11, 7/9, 8/9
(c) 3/5, 2/3, 7/9, 9/11, 8/9 (d) 8/9, 9/11, 7/9, 2/3, 3/5
13. 337.62 + 8.591 + 34.4  = ? [2012-I]
(a) 370.611 (b) 380.511
(c) 380.611 (d) 426.97
14. Find the sum of :- 1/9+1/6+1/12+1/72 [2012-I]
(a) 3/5 (b) 3/2
(c) 3/8 (d) 4/7
15. ? % of 932 + 30 = 309.6 [2012-I]
(a) 25 (b) 3 0
(c) 35 (d) 4 0
16. The difference between a number and its two-fifth is 510.
What is 10% of that number ? [2012-I]
(a) 12.75 (b) 8 5
(c) 2 04 (d) None
17. If 4/5
th
 of an estate is worth ` 16,800, then the value of 3/7
th
of the estate is [2012-I]
(a) ` 9000 (b) ` 21000
(c) ` 72000 (d) ` 90000
18. If a/b = 3/4 and 8a + 5b=22, then the value of ‘a’ is [2012-I]
(a)1 (b) 1/2 (c) 3/2 (d) 3/4
19. If (a – b) is 6 more than (c + d) and (a + b) is 3 less than
(c – d), then the value of (a – c) is [2012-I]
(a) 0.5 (b) 1.0
(c) 1.5 (d) 2.0
20. The number whose square is equal to the difference of the
squares of 40 and 32 is [2012-II]
(a) 45.09 (b) 24
(c) 25 (d) 28
Number System/Simplification
21. 15 buckets of water fill a tank when the capacity of each
bucket is 7 litres How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 5 litres ?[2012-II]
(a) 12 (b) 24
(c) 21 (d) 30
22. A vessel, full of water, weighs 27.5 kg. when the vessel
is  1/4 full, it weighs 12.26 kg.  Find the weight of empty vessel
? [2012-II]
(a) 7.18 kg (b) 6.54 kg
(c) 2.75 kg (d) 2 5 kg
23. If a+b = 10 and ab = 21, find the value of a
3
+b
3
[2012-II]
(a) 370 (b) 210
(c) 730 (d) 598
24. If a/(a+b)=17/23, what is (a+b)/(a – b) equal to ? [2012-II]
(a) 13/7 (b) 23/11
(c) 14/5 (d) 25/9
25.
2
(598 479) (598 479)
(598 479)
2
+ --
´
[2012-II]
(a) 2 (b) 6
(c) 4 (d) 8
26. A jar contains b lack and white marbles. If there are ten marbles
in the jar, then which of the following could not be the ratio
of black to white marbles ? [2012-II]
(a) 9:1 (b) 7:3
(c) 1:10 (d) 6:4
27. The number whose square is equal to the difference of the
squares of 37 and 23 is [2013-I]
(a) 45.09 (b) 28.98
(c) 47.09 (d) 2 8
28. A vessel, full of water, weights 24 kg. When the vessel is
1/4 full, it weighs 9 kg. Find the weight of empty vessel.
[2013-I]
(a) 4 kg (b) 5 kg
(c) 8 kg (d) 3 kg
29. If a – b = 4 and ab = 45 find the value of a
3
 – b
3
. [2013-I]
(a) 6 04 (b) 370
(c) 2 53 (d) 199
30. If a/(a + b) = 15/21, what is (a + b)/(a – b) equal to ? [2013-I]
(a) 13/9 (b) 23/11
(c) 14/5 (d) 21/9
31.
( )( )
( )
22
798 579 798 579
798 579
+ --
´
 = ? [2013-I]
(a)2 (b) 6
(c)4 (d) 8
32. 18 buckets of water fill a tank when the capacity of each
bucket is 8 litres. How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 12 litres ?[2013-I]
( a) 12
(b) 13.5
(c) 24
(d) can not be determined due to insufficient data
33. Find two natural numbers whose sum is 85 and the least
common multiple is 102. [2014-I]
(a) 30 and 55 (b) 17 and 68
(c) 35 and 55 (d) 51 and 34
34. In a fort there was sufficient food for 200 soldiers for 31
days. After 27 days, 120 soldiers left the fort. For how many
extra days will the rest of the food last for the remaining
soldiers ? [2014-I]
(a) 12 days (b) 10 days
(c) 8 days (d) 6 days
35. 10 is added to a certain number, the sum is multiplied
by 7, the product is divided by 5 and 5 is subtracted from
the quotient. The remainder left is half of 88. What is the
number ? [2014-I]
( a) 21 (b) 2 0 (c ) 25 (d) 3 0
36. A bag contains 25 paise, 50 paise and 1 ` coins. There are
220 coins in all and the total amount in the bag is ` 160. If
there are thrice as many 1 ` coins as there are 25 paise coins,
then what is the number of 50 paise coins ? [2014-I]
(a) 60 (b) 4 0 (c) 1 20 (d) 8 0
37. The sum of two numbers is equal to thrice their difference. If
the smaller of the numbers is 10 find the other number.
[2014-I]
( a) 15 (b) 3 0
(c) 40 (d) None of these.
 38. Simplify:
69 69 69 65 65 65
69 69 69 65 65 65
´ ´ - ´´
´ + ´+´
[2014-I]
(a)1 (b) 4
(c) 0.216 (d) 0.164
39. 7 is added to a certain number, the sum is multiplied by 5;
the product is divided by  9 and 3 is subtracted from the
quotient. The remainder left is 12. What is the number ?
[2014-II]
( a) 20 (b) 3 0
(c) 40 (d) 5
40. How many digits will be there to the right of the decimal
point in the product of  95.75 and 0.02554 ? [2014-II]
(a)5 (b) 6
(c)7 (d) Insufficient data
41. The average weight of 50 boys in a class is 45 kg. When one
boy leaves the class, the average reduces by 100g. Find the
weight of the boy who left the class. [2015-II]
(a) 50 kg. (b) 50.8 kg
(c) 49 kg (d) 49.9 kg
42. In Arun's opinion, his weight is greater than 65 kg but less
than 72 kg. His brother doest not agree with Arun and he
thinks that Arun's weight is greater than 60 kg but less than
70 kg. His mother's view is that his weight cannot be greater
than 68 kg. If all are them are correct in their estimation, what
is the average of different probable weights of Arun?
[2016-I]
(a) 67 kg (b) 68 kg
(c) 69 kg (d) data inadequate
Page 3


Number System/
Simplification
1
1. In a 225 meter long yard 26 trees are planted at equal distance,
one tree being at each end of the yard. What is the distance
between two consecutive trees ? [2011-I]
(a) 10 meters (b) 8 meters
(c) 12 meters (d) 9 meters
2. A bonus of ` 1000 is divided among three employ ees. Rohit gets
twice the amount Sachin gets. Sachin gets one fifth of what
Gagan gets. How much amount does Gagan get ? [2011-I]
(a) ` 500 (b) ` 625
(c) ` 750 (d) ` 120
3. A boy was asked to multiply a number by 25. Instead, he
multiplied the number by 52 and got the answer 324 more
than the correct answer. The number to be multiplied was
[2011-I]
( a) 12 (b) 1 5 (c) 25 (d) 3 2
4. The value of (?) in the equation 365.089 – ? + 89.72 = 302.35 is
[2011-I]
(a) 152.456 (b) 152.459
(c) 153.456 (d) 153.459
5. A sum of ` 312 is divided among 60 boys and some girls in
such a way that each boy gets ` 3.60 and each girl gets
` 2.40. The number of girls are- [2011-I]
(a) 35 (b) 6 0
(c) 40 (d) 6 5
6. The number of girls in a class in five times the number of
boys. Which of the following cannot be the total number of
children in the class ? [2011-II]
(a) 24 (b) 3 0
(c) 35 (d) 5 4
7. Ram went to a shop to buy 50 kg of rice. He bought two
varieties of rice which cost him ` 4.50 per kg and ` 5 per kg.
He spent a total of ` 240. What was the quantity of the
cheaper rice purchased by him ? [2011-II]
(a) 20 Kg (b) 25 Kg
(c) 30 Kg (d) None of these
8. A man has ` 640 in the denominations of one rupee, five
rupee and ten rupee notes. The number of each type of
notes are equal. What is the total number of notes he has ?
[2011-II]
(a) 60 (b) 1 50 (c) 90 (d) 1 20
9. A man has few hens and cows. If the total number of heads
are 48 and the total number of feet are 140, then the number
of hens are [2011-II]
(a) 22 (b) 23
(c) 24 (d) 26
10. A student was asked to divide a number by 3. But, instead
of dividing it he multiplied it by 3 and got 29.7 as the answer.
What was the correct answer had he not made the mistake ?
[2011-II]
(a) 3.3 (b) 9.3
(c) 9.8 (d) 9.9
11. Which of the following fraction is the smallest ? [2011-II]
(a) 9/13 (b) 17/26
(c) 28/39 (d) 33/52
12. Which of the following fractions are in ascending order ?
[2012-I]
(a) 2/3, 3/5,7/9,9/11,8/9 (b) 3/5, 2/3, 9/11, 7/9, 8/9
(c) 3/5, 2/3, 7/9, 9/11, 8/9 (d) 8/9, 9/11, 7/9, 2/3, 3/5
13. 337.62 + 8.591 + 34.4  = ? [2012-I]
(a) 370.611 (b) 380.511
(c) 380.611 (d) 426.97
14. Find the sum of :- 1/9+1/6+1/12+1/72 [2012-I]
(a) 3/5 (b) 3/2
(c) 3/8 (d) 4/7
15. ? % of 932 + 30 = 309.6 [2012-I]
(a) 25 (b) 3 0
(c) 35 (d) 4 0
16. The difference between a number and its two-fifth is 510.
What is 10% of that number ? [2012-I]
(a) 12.75 (b) 8 5
(c) 2 04 (d) None
17. If 4/5
th
 of an estate is worth ` 16,800, then the value of 3/7
th
of the estate is [2012-I]
(a) ` 9000 (b) ` 21000
(c) ` 72000 (d) ` 90000
18. If a/b = 3/4 and 8a + 5b=22, then the value of ‘a’ is [2012-I]
(a)1 (b) 1/2 (c) 3/2 (d) 3/4
19. If (a – b) is 6 more than (c + d) and (a + b) is 3 less than
(c – d), then the value of (a – c) is [2012-I]
(a) 0.5 (b) 1.0
(c) 1.5 (d) 2.0
20. The number whose square is equal to the difference of the
squares of 40 and 32 is [2012-II]
(a) 45.09 (b) 24
(c) 25 (d) 28
Number System/Simplification
21. 15 buckets of water fill a tank when the capacity of each
bucket is 7 litres How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 5 litres ?[2012-II]
(a) 12 (b) 24
(c) 21 (d) 30
22. A vessel, full of water, weighs 27.5 kg. when the vessel
is  1/4 full, it weighs 12.26 kg.  Find the weight of empty vessel
? [2012-II]
(a) 7.18 kg (b) 6.54 kg
(c) 2.75 kg (d) 2 5 kg
23. If a+b = 10 and ab = 21, find the value of a
3
+b
3
[2012-II]
(a) 370 (b) 210
(c) 730 (d) 598
24. If a/(a+b)=17/23, what is (a+b)/(a – b) equal to ? [2012-II]
(a) 13/7 (b) 23/11
(c) 14/5 (d) 25/9
25.
2
(598 479) (598 479)
(598 479)
2
+ --
´
[2012-II]
(a) 2 (b) 6
(c) 4 (d) 8
26. A jar contains b lack and white marbles. If there are ten marbles
in the jar, then which of the following could not be the ratio
of black to white marbles ? [2012-II]
(a) 9:1 (b) 7:3
(c) 1:10 (d) 6:4
27. The number whose square is equal to the difference of the
squares of 37 and 23 is [2013-I]
(a) 45.09 (b) 28.98
(c) 47.09 (d) 2 8
28. A vessel, full of water, weights 24 kg. When the vessel is
1/4 full, it weighs 9 kg. Find the weight of empty vessel.
[2013-I]
(a) 4 kg (b) 5 kg
(c) 8 kg (d) 3 kg
29. If a – b = 4 and ab = 45 find the value of a
3
 – b
3
. [2013-I]
(a) 6 04 (b) 370
(c) 2 53 (d) 199
30. If a/(a + b) = 15/21, what is (a + b)/(a – b) equal to ? [2013-I]
(a) 13/9 (b) 23/11
(c) 14/5 (d) 21/9
31.
( )( )
( )
22
798 579 798 579
798 579
+ --
´
 = ? [2013-I]
(a)2 (b) 6
(c)4 (d) 8
32. 18 buckets of water fill a tank when the capacity of each
bucket is 8 litres. How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 12 litres ?[2013-I]
( a) 12
(b) 13.5
(c) 24
(d) can not be determined due to insufficient data
33. Find two natural numbers whose sum is 85 and the least
common multiple is 102. [2014-I]
(a) 30 and 55 (b) 17 and 68
(c) 35 and 55 (d) 51 and 34
34. In a fort there was sufficient food for 200 soldiers for 31
days. After 27 days, 120 soldiers left the fort. For how many
extra days will the rest of the food last for the remaining
soldiers ? [2014-I]
(a) 12 days (b) 10 days
(c) 8 days (d) 6 days
35. 10 is added to a certain number, the sum is multiplied
by 7, the product is divided by 5 and 5 is subtracted from
the quotient. The remainder left is half of 88. What is the
number ? [2014-I]
( a) 21 (b) 2 0 (c ) 25 (d) 3 0
36. A bag contains 25 paise, 50 paise and 1 ` coins. There are
220 coins in all and the total amount in the bag is ` 160. If
there are thrice as many 1 ` coins as there are 25 paise coins,
then what is the number of 50 paise coins ? [2014-I]
(a) 60 (b) 4 0 (c) 1 20 (d) 8 0
37. The sum of two numbers is equal to thrice their difference. If
the smaller of the numbers is 10 find the other number.
[2014-I]
( a) 15 (b) 3 0
(c) 40 (d) None of these.
 38. Simplify:
69 69 69 65 65 65
69 69 69 65 65 65
´ ´ - ´´
´ + ´+´
[2014-I]
(a)1 (b) 4
(c) 0.216 (d) 0.164
39. 7 is added to a certain number, the sum is multiplied by 5;
the product is divided by  9 and 3 is subtracted from the
quotient. The remainder left is 12. What is the number ?
[2014-II]
( a) 20 (b) 3 0
(c) 40 (d) 5
40. How many digits will be there to the right of the decimal
point in the product of  95.75 and 0.02554 ? [2014-II]
(a)5 (b) 6
(c)7 (d) Insufficient data
41. The average weight of 50 boys in a class is 45 kg. When one
boy leaves the class, the average reduces by 100g. Find the
weight of the boy who left the class. [2015-II]
(a) 50 kg. (b) 50.8 kg
(c) 49 kg (d) 49.9 kg
42. In Arun's opinion, his weight is greater than 65 kg but less
than 72 kg. His brother doest not agree with Arun and he
thinks that Arun's weight is greater than 60 kg but less than
70 kg. His mother's view is that his weight cannot be greater
than 68 kg. If all are them are correct in their estimation, what
is the average of different probable weights of Arun?
[2016-I]
(a) 67 kg (b) 68 kg
(c) 69 kg (d) data inadequate
Number System/Simplification
43. Present age of X and Y are in the ratio 7:5 respectively . Four
years hence, the ratio of their ages will become 11:9
respectively. What is the present age of Y? [2016-I]
(a) 1 year (b) 7 year
(c) 5 year (d) None of these
44. In an examination, a student was asked to find 
3
14
 of a
certain number. By mistake, he found 
3
4
of it. His answer
was 150 more than the correct answer. Find the number.
[2016 - II]
(a) 1 80 (b) 2 80
(c) 3 80 (d) 4 80
45. A crate of mangoes contains one bruised mango for every
30 mangoes in the crate. If 3 out of every 4 bruised mangoes
are considered unsalable, and there are 12 unsalable
mangoes in the crate, how many mangoes are there in the
crate? [2016 - II]
(a) 4 80 (b) 5 00
(c) 4 20 (d) 5 20
46. The mean of 50 observations was 36. It was found later that
an observation 48 was wrongly taken as 23. The corrected
new mean is [2016 - II]
(a) 35.2 (b) 34.1
(c) 36.5 (d) 39.1
47. The average score of a cricketer for ten matches is 38.9 runs.
If the average for the first six matches is 42, the average for
the last four matches is [2016 - II]
(a) 33.25 (b) 33.5
(c) 34.25 (d) 3 5
48. If A/B = 4/3 then what is the value of (9A–3B)/(9A+3B) is
[2017 - I]
(a) 3/5 (b) 5/3
(c) 2/5 (d) 3/7
49. If one student got 77/100, 96/150 and 103/350 in various
subjects, what is the percentage average? [2017 - I]
(a) 15.33% (b) 12.25%
(c)  16.33% (d) 18.15%
50. In an election between two candidates, Biku got 55% votes
of the total valid votes, 25% of the votes were declared
invalid. If total populations of the village were  6000. Find
the valid votes that Mahtre got, was [2017 - I]
(a) 1575 (b) 2025
(c) 2075 (d) 2175
51.  If 30% of a number is subtracted from 91 gives the same
number, find the number. [2017 - I]
(a) 80 (b) 9 0
(c) 70 (d) 6 0
52. If 50% of a number is added to 84 gives the same number,
what is the number? [2017 - I]
(a) 1 78 (b) 1 74
(c) 158 (d) 1 6 8
53. If 381A is divisible by 9, what is the least natural number A?
[2017 - I]
(a)6 (b) 1
(c)9 (d) 4
54. If a number exceeds 40% of itself by 56, then what is the
number? [2017 - II]
(a) 1 50 (b) 1 30
(c) 1 60 (d) 1 40
55. Average weight of 15 students increased by 1.5 kg when
one person of 40 kg is replaced by a new man. Then weight
of the new man is [2017 - II]
(a) 62.5 kg (b) 58.5 kg
(c) 72.5 kg (d) 54.5 kg
56. Average temperature of Tuesday to Thursday was 38 degree
celsius and that Wednesday to Friday was 37 degree celsius.
If the temperature on Friday was 39 degree celsius. The
temperature on Tuesday was? [2017 - II]
(a) 38 degree celsius (b) 36 degree celsius
(c) 42 degree celsius (d) 39 degree celsius
57. A men spend 1/3 of his income on food,1/4 of the rest on
rent and 1/5 of the rest on clothes. He still has Rs.1760 left
with him. Find his income? [2017 - II]
(a) 4400 (b) 4200
(c) 4800 (d) 5200
58. Two numbers are in the ratio 12 : 13. If 20 is subtracted from
each, the new numbers are in the ratio 2 : 3. The smaller
number is: [2017 - II]
(a) 26 (b) 2 4
(c) 32 (d) 2 8
59. The sum of two numbers is 36 and their H.C.F and L.C.M. are
3 and 105 respectively. The sum of the reciprocals of two
numbers is     [2018 - I]
(a)
2
35
(b)
3
25
(c)
4
35
(d)
2
25
60. A teacher wants to arrange his students in an equal number
of rows and columns. If there are 1369 students, the number
of students in the last row are     [2018 - I]
(a) 37 (b) 33 (c) 63 (d) 47
61. A farmer divides his herd of n cows among his four sons, so
that the first son gets one–half the herd, the second one–
fourth, the third son 
1
5
 and the fourth son 7 cows. Then the
value of n is     [2018 - I]
(a) 2 40 (b) 100 (c) 1 80 (d) 140
62. The average of 5/16 and 3/8 is__?             [2018 - II]
(a) 0.5425 (b) 0.2585
(c) 0.3475 (d) 0.4385
63. Find the value of  
0.0081
 + 
0.0064
 ?           [2018 - II]
(a) 0.27 (b) 0.7
(c) 0.17 (d) 0.4
Page 4


Number System/
Simplification
1
1. In a 225 meter long yard 26 trees are planted at equal distance,
one tree being at each end of the yard. What is the distance
between two consecutive trees ? [2011-I]
(a) 10 meters (b) 8 meters
(c) 12 meters (d) 9 meters
2. A bonus of ` 1000 is divided among three employ ees. Rohit gets
twice the amount Sachin gets. Sachin gets one fifth of what
Gagan gets. How much amount does Gagan get ? [2011-I]
(a) ` 500 (b) ` 625
(c) ` 750 (d) ` 120
3. A boy was asked to multiply a number by 25. Instead, he
multiplied the number by 52 and got the answer 324 more
than the correct answer. The number to be multiplied was
[2011-I]
( a) 12 (b) 1 5 (c) 25 (d) 3 2
4. The value of (?) in the equation 365.089 – ? + 89.72 = 302.35 is
[2011-I]
(a) 152.456 (b) 152.459
(c) 153.456 (d) 153.459
5. A sum of ` 312 is divided among 60 boys and some girls in
such a way that each boy gets ` 3.60 and each girl gets
` 2.40. The number of girls are- [2011-I]
(a) 35 (b) 6 0
(c) 40 (d) 6 5
6. The number of girls in a class in five times the number of
boys. Which of the following cannot be the total number of
children in the class ? [2011-II]
(a) 24 (b) 3 0
(c) 35 (d) 5 4
7. Ram went to a shop to buy 50 kg of rice. He bought two
varieties of rice which cost him ` 4.50 per kg and ` 5 per kg.
He spent a total of ` 240. What was the quantity of the
cheaper rice purchased by him ? [2011-II]
(a) 20 Kg (b) 25 Kg
(c) 30 Kg (d) None of these
8. A man has ` 640 in the denominations of one rupee, five
rupee and ten rupee notes. The number of each type of
notes are equal. What is the total number of notes he has ?
[2011-II]
(a) 60 (b) 1 50 (c) 90 (d) 1 20
9. A man has few hens and cows. If the total number of heads
are 48 and the total number of feet are 140, then the number
of hens are [2011-II]
(a) 22 (b) 23
(c) 24 (d) 26
10. A student was asked to divide a number by 3. But, instead
of dividing it he multiplied it by 3 and got 29.7 as the answer.
What was the correct answer had he not made the mistake ?
[2011-II]
(a) 3.3 (b) 9.3
(c) 9.8 (d) 9.9
11. Which of the following fraction is the smallest ? [2011-II]
(a) 9/13 (b) 17/26
(c) 28/39 (d) 33/52
12. Which of the following fractions are in ascending order ?
[2012-I]
(a) 2/3, 3/5,7/9,9/11,8/9 (b) 3/5, 2/3, 9/11, 7/9, 8/9
(c) 3/5, 2/3, 7/9, 9/11, 8/9 (d) 8/9, 9/11, 7/9, 2/3, 3/5
13. 337.62 + 8.591 + 34.4  = ? [2012-I]
(a) 370.611 (b) 380.511
(c) 380.611 (d) 426.97
14. Find the sum of :- 1/9+1/6+1/12+1/72 [2012-I]
(a) 3/5 (b) 3/2
(c) 3/8 (d) 4/7
15. ? % of 932 + 30 = 309.6 [2012-I]
(a) 25 (b) 3 0
(c) 35 (d) 4 0
16. The difference between a number and its two-fifth is 510.
What is 10% of that number ? [2012-I]
(a) 12.75 (b) 8 5
(c) 2 04 (d) None
17. If 4/5
th
 of an estate is worth ` 16,800, then the value of 3/7
th
of the estate is [2012-I]
(a) ` 9000 (b) ` 21000
(c) ` 72000 (d) ` 90000
18. If a/b = 3/4 and 8a + 5b=22, then the value of ‘a’ is [2012-I]
(a)1 (b) 1/2 (c) 3/2 (d) 3/4
19. If (a – b) is 6 more than (c + d) and (a + b) is 3 less than
(c – d), then the value of (a – c) is [2012-I]
(a) 0.5 (b) 1.0
(c) 1.5 (d) 2.0
20. The number whose square is equal to the difference of the
squares of 40 and 32 is [2012-II]
(a) 45.09 (b) 24
(c) 25 (d) 28
Number System/Simplification
21. 15 buckets of water fill a tank when the capacity of each
bucket is 7 litres How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 5 litres ?[2012-II]
(a) 12 (b) 24
(c) 21 (d) 30
22. A vessel, full of water, weighs 27.5 kg. when the vessel
is  1/4 full, it weighs 12.26 kg.  Find the weight of empty vessel
? [2012-II]
(a) 7.18 kg (b) 6.54 kg
(c) 2.75 kg (d) 2 5 kg
23. If a+b = 10 and ab = 21, find the value of a
3
+b
3
[2012-II]
(a) 370 (b) 210
(c) 730 (d) 598
24. If a/(a+b)=17/23, what is (a+b)/(a – b) equal to ? [2012-II]
(a) 13/7 (b) 23/11
(c) 14/5 (d) 25/9
25.
2
(598 479) (598 479)
(598 479)
2
+ --
´
[2012-II]
(a) 2 (b) 6
(c) 4 (d) 8
26. A jar contains b lack and white marbles. If there are ten marbles
in the jar, then which of the following could not be the ratio
of black to white marbles ? [2012-II]
(a) 9:1 (b) 7:3
(c) 1:10 (d) 6:4
27. The number whose square is equal to the difference of the
squares of 37 and 23 is [2013-I]
(a) 45.09 (b) 28.98
(c) 47.09 (d) 2 8
28. A vessel, full of water, weights 24 kg. When the vessel is
1/4 full, it weighs 9 kg. Find the weight of empty vessel.
[2013-I]
(a) 4 kg (b) 5 kg
(c) 8 kg (d) 3 kg
29. If a – b = 4 and ab = 45 find the value of a
3
 – b
3
. [2013-I]
(a) 6 04 (b) 370
(c) 2 53 (d) 199
30. If a/(a + b) = 15/21, what is (a + b)/(a – b) equal to ? [2013-I]
(a) 13/9 (b) 23/11
(c) 14/5 (d) 21/9
31.
( )( )
( )
22
798 579 798 579
798 579
+ --
´
 = ? [2013-I]
(a)2 (b) 6
(c)4 (d) 8
32. 18 buckets of water fill a tank when the capacity of each
bucket is 8 litres. How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 12 litres ?[2013-I]
( a) 12
(b) 13.5
(c) 24
(d) can not be determined due to insufficient data
33. Find two natural numbers whose sum is 85 and the least
common multiple is 102. [2014-I]
(a) 30 and 55 (b) 17 and 68
(c) 35 and 55 (d) 51 and 34
34. In a fort there was sufficient food for 200 soldiers for 31
days. After 27 days, 120 soldiers left the fort. For how many
extra days will the rest of the food last for the remaining
soldiers ? [2014-I]
(a) 12 days (b) 10 days
(c) 8 days (d) 6 days
35. 10 is added to a certain number, the sum is multiplied
by 7, the product is divided by 5 and 5 is subtracted from
the quotient. The remainder left is half of 88. What is the
number ? [2014-I]
( a) 21 (b) 2 0 (c ) 25 (d) 3 0
36. A bag contains 25 paise, 50 paise and 1 ` coins. There are
220 coins in all and the total amount in the bag is ` 160. If
there are thrice as many 1 ` coins as there are 25 paise coins,
then what is the number of 50 paise coins ? [2014-I]
(a) 60 (b) 4 0 (c) 1 20 (d) 8 0
37. The sum of two numbers is equal to thrice their difference. If
the smaller of the numbers is 10 find the other number.
[2014-I]
( a) 15 (b) 3 0
(c) 40 (d) None of these.
 38. Simplify:
69 69 69 65 65 65
69 69 69 65 65 65
´ ´ - ´´
´ + ´+´
[2014-I]
(a)1 (b) 4
(c) 0.216 (d) 0.164
39. 7 is added to a certain number, the sum is multiplied by 5;
the product is divided by  9 and 3 is subtracted from the
quotient. The remainder left is 12. What is the number ?
[2014-II]
( a) 20 (b) 3 0
(c) 40 (d) 5
40. How many digits will be there to the right of the decimal
point in the product of  95.75 and 0.02554 ? [2014-II]
(a)5 (b) 6
(c)7 (d) Insufficient data
41. The average weight of 50 boys in a class is 45 kg. When one
boy leaves the class, the average reduces by 100g. Find the
weight of the boy who left the class. [2015-II]
(a) 50 kg. (b) 50.8 kg
(c) 49 kg (d) 49.9 kg
42. In Arun's opinion, his weight is greater than 65 kg but less
than 72 kg. His brother doest not agree with Arun and he
thinks that Arun's weight is greater than 60 kg but less than
70 kg. His mother's view is that his weight cannot be greater
than 68 kg. If all are them are correct in their estimation, what
is the average of different probable weights of Arun?
[2016-I]
(a) 67 kg (b) 68 kg
(c) 69 kg (d) data inadequate
Number System/Simplification
43. Present age of X and Y are in the ratio 7:5 respectively . Four
years hence, the ratio of their ages will become 11:9
respectively. What is the present age of Y? [2016-I]
(a) 1 year (b) 7 year
(c) 5 year (d) None of these
44. In an examination, a student was asked to find 
3
14
 of a
certain number. By mistake, he found 
3
4
of it. His answer
was 150 more than the correct answer. Find the number.
[2016 - II]
(a) 1 80 (b) 2 80
(c) 3 80 (d) 4 80
45. A crate of mangoes contains one bruised mango for every
30 mangoes in the crate. If 3 out of every 4 bruised mangoes
are considered unsalable, and there are 12 unsalable
mangoes in the crate, how many mangoes are there in the
crate? [2016 - II]
(a) 4 80 (b) 5 00
(c) 4 20 (d) 5 20
46. The mean of 50 observations was 36. It was found later that
an observation 48 was wrongly taken as 23. The corrected
new mean is [2016 - II]
(a) 35.2 (b) 34.1
(c) 36.5 (d) 39.1
47. The average score of a cricketer for ten matches is 38.9 runs.
If the average for the first six matches is 42, the average for
the last four matches is [2016 - II]
(a) 33.25 (b) 33.5
(c) 34.25 (d) 3 5
48. If A/B = 4/3 then what is the value of (9A–3B)/(9A+3B) is
[2017 - I]
(a) 3/5 (b) 5/3
(c) 2/5 (d) 3/7
49. If one student got 77/100, 96/150 and 103/350 in various
subjects, what is the percentage average? [2017 - I]
(a) 15.33% (b) 12.25%
(c)  16.33% (d) 18.15%
50. In an election between two candidates, Biku got 55% votes
of the total valid votes, 25% of the votes were declared
invalid. If total populations of the village were  6000. Find
the valid votes that Mahtre got, was [2017 - I]
(a) 1575 (b) 2025
(c) 2075 (d) 2175
51.  If 30% of a number is subtracted from 91 gives the same
number, find the number. [2017 - I]
(a) 80 (b) 9 0
(c) 70 (d) 6 0
52. If 50% of a number is added to 84 gives the same number,
what is the number? [2017 - I]
(a) 1 78 (b) 1 74
(c) 158 (d) 1 6 8
53. If 381A is divisible by 9, what is the least natural number A?
[2017 - I]
(a)6 (b) 1
(c)9 (d) 4
54. If a number exceeds 40% of itself by 56, then what is the
number? [2017 - II]
(a) 1 50 (b) 1 30
(c) 1 60 (d) 1 40
55. Average weight of 15 students increased by 1.5 kg when
one person of 40 kg is replaced by a new man. Then weight
of the new man is [2017 - II]
(a) 62.5 kg (b) 58.5 kg
(c) 72.5 kg (d) 54.5 kg
56. Average temperature of Tuesday to Thursday was 38 degree
celsius and that Wednesday to Friday was 37 degree celsius.
If the temperature on Friday was 39 degree celsius. The
temperature on Tuesday was? [2017 - II]
(a) 38 degree celsius (b) 36 degree celsius
(c) 42 degree celsius (d) 39 degree celsius
57. A men spend 1/3 of his income on food,1/4 of the rest on
rent and 1/5 of the rest on clothes. He still has Rs.1760 left
with him. Find his income? [2017 - II]
(a) 4400 (b) 4200
(c) 4800 (d) 5200
58. Two numbers are in the ratio 12 : 13. If 20 is subtracted from
each, the new numbers are in the ratio 2 : 3. The smaller
number is: [2017 - II]
(a) 26 (b) 2 4
(c) 32 (d) 2 8
59. The sum of two numbers is 36 and their H.C.F and L.C.M. are
3 and 105 respectively. The sum of the reciprocals of two
numbers is     [2018 - I]
(a)
2
35
(b)
3
25
(c)
4
35
(d)
2
25
60. A teacher wants to arrange his students in an equal number
of rows and columns. If there are 1369 students, the number
of students in the last row are     [2018 - I]
(a) 37 (b) 33 (c) 63 (d) 47
61. A farmer divides his herd of n cows among his four sons, so
that the first son gets one–half the herd, the second one–
fourth, the third son 
1
5
 and the fourth son 7 cows. Then the
value of n is     [2018 - I]
(a) 2 40 (b) 100 (c) 1 80 (d) 140
62. The average of 5/16 and 3/8 is__?             [2018 - II]
(a) 0.5425 (b) 0.2585
(c) 0.3475 (d) 0.4385
63. Find the value of  
0.0081
 + 
0.0064
 ?           [2018 - II]
(a) 0.27 (b) 0.7
(c) 0.17 (d) 0.4
Number System/Simplification
64. Find the value of  216
0.16
 × 16
0.18
 ?              [2018 - II]
(a)4 (b) 6
(c)8 (d) 2
65. If 
(a 8) (2a 1)
3 27
++
=
, then find 'a'?             [2018 - II]
(a)1 (b) 0
(c) –1 (d) 0.5
66. If 
2
 = 1.4142, find the value of
11
222
2 2 22
+++
+-
[2019-I]
(a) 1.4144 (b) 2.8284
(c) 28.284 (d) 2.4142
67. In an examination, a student was asked to find 
3
14
 of a certain
number. By mistake, he found 
3
4
of it. His answer was 150
more than the correct answer. Find the number. [2019 - II]
(a) 1 80 (b) 2 80
(c) 3 80 (d) 4 80
68.
5 6 83 31 7
? 1 32
67 9 54 3 9
¸´ - ¸ +´ = [2019 - II]
(a)
7
6
(b)
6
7
(c)1 (d) None of these
69. The whole number which is a multiple of every number is
[2019 - II]
(a)0
(b) 1
(c) There is no such number
(d) None of these
70. Highest common factor of 42 and 162 is ___. [2019 - II]
(a)6 (b) 4
(c) 12 (d) 2
71. The ratio betw een two numb ers is 3 : 4. If each numb er is increased
by 6 the ratio becomes 4 : 5. The diff erence betw een the numbers is
[2019 - II]
(a)1 (b) 3
(c)6 (d) 8
72. If A = x% of y and B = y% of x, then which of the following
is true? [2020 - I]
(a) A is smaller than B.
(b) A is greater than B
(c) None of these
(d) If x is smaller than y , then A is greater than B.
73. If 20% of A = B, then B% of 20 is the same as: [2020 - I]
(a) 4% of A (b) 5% of A
(c) 20% of A (d) None of these
74. The sum of ages of 5 children born at the intervals of 3 years
each is 50 years. What is the age of the youngest child?
[2020 - I]
(a) 4 years (b) 5 years
(c) 8 years (d) 10 years
75. The average weight of 8 person’s increases by 2.5 kg when
a new person comes in place of one of them weighing 65 kg.
What might be the weight of the new person? [2020 - I]
(a) 76kg (b) 76.5kg
(c) 85kg (d) Data inadequate
76. Present ages of Sameer and Anand are in the ratio of 5 : 4
respectively. Three years hence, the ratio of their ages will
become 11 : 9 respectively. What is Anand’s present age in
years? [2020 - I]
(a) 24 years (b) 27 years
(c) 40 years (d) Cannot be determined
77. What should come in place of both x in the equation
162
=
128
x
x
[2020 - I]
(a) 12 (b) 14
(c) 1 44 (d) 196
78. The value of 
0.1 0.1 0.1 0.02 0.02 0.02
0.2 0.2 0.2 0.04 0.04 0.04
´ ´ +´´
´ ´ +´´
 is?
[2020 - I]
(a) 0.0125 (b) 2 5
(c) 0.25 (d) 0.125
Page 5


Number System/
Simplification
1
1. In a 225 meter long yard 26 trees are planted at equal distance,
one tree being at each end of the yard. What is the distance
between two consecutive trees ? [2011-I]
(a) 10 meters (b) 8 meters
(c) 12 meters (d) 9 meters
2. A bonus of ` 1000 is divided among three employ ees. Rohit gets
twice the amount Sachin gets. Sachin gets one fifth of what
Gagan gets. How much amount does Gagan get ? [2011-I]
(a) ` 500 (b) ` 625
(c) ` 750 (d) ` 120
3. A boy was asked to multiply a number by 25. Instead, he
multiplied the number by 52 and got the answer 324 more
than the correct answer. The number to be multiplied was
[2011-I]
( a) 12 (b) 1 5 (c) 25 (d) 3 2
4. The value of (?) in the equation 365.089 – ? + 89.72 = 302.35 is
[2011-I]
(a) 152.456 (b) 152.459
(c) 153.456 (d) 153.459
5. A sum of ` 312 is divided among 60 boys and some girls in
such a way that each boy gets ` 3.60 and each girl gets
` 2.40. The number of girls are- [2011-I]
(a) 35 (b) 6 0
(c) 40 (d) 6 5
6. The number of girls in a class in five times the number of
boys. Which of the following cannot be the total number of
children in the class ? [2011-II]
(a) 24 (b) 3 0
(c) 35 (d) 5 4
7. Ram went to a shop to buy 50 kg of rice. He bought two
varieties of rice which cost him ` 4.50 per kg and ` 5 per kg.
He spent a total of ` 240. What was the quantity of the
cheaper rice purchased by him ? [2011-II]
(a) 20 Kg (b) 25 Kg
(c) 30 Kg (d) None of these
8. A man has ` 640 in the denominations of one rupee, five
rupee and ten rupee notes. The number of each type of
notes are equal. What is the total number of notes he has ?
[2011-II]
(a) 60 (b) 1 50 (c) 90 (d) 1 20
9. A man has few hens and cows. If the total number of heads
are 48 and the total number of feet are 140, then the number
of hens are [2011-II]
(a) 22 (b) 23
(c) 24 (d) 26
10. A student was asked to divide a number by 3. But, instead
of dividing it he multiplied it by 3 and got 29.7 as the answer.
What was the correct answer had he not made the mistake ?
[2011-II]
(a) 3.3 (b) 9.3
(c) 9.8 (d) 9.9
11. Which of the following fraction is the smallest ? [2011-II]
(a) 9/13 (b) 17/26
(c) 28/39 (d) 33/52
12. Which of the following fractions are in ascending order ?
[2012-I]
(a) 2/3, 3/5,7/9,9/11,8/9 (b) 3/5, 2/3, 9/11, 7/9, 8/9
(c) 3/5, 2/3, 7/9, 9/11, 8/9 (d) 8/9, 9/11, 7/9, 2/3, 3/5
13. 337.62 + 8.591 + 34.4  = ? [2012-I]
(a) 370.611 (b) 380.511
(c) 380.611 (d) 426.97
14. Find the sum of :- 1/9+1/6+1/12+1/72 [2012-I]
(a) 3/5 (b) 3/2
(c) 3/8 (d) 4/7
15. ? % of 932 + 30 = 309.6 [2012-I]
(a) 25 (b) 3 0
(c) 35 (d) 4 0
16. The difference between a number and its two-fifth is 510.
What is 10% of that number ? [2012-I]
(a) 12.75 (b) 8 5
(c) 2 04 (d) None
17. If 4/5
th
 of an estate is worth ` 16,800, then the value of 3/7
th
of the estate is [2012-I]
(a) ` 9000 (b) ` 21000
(c) ` 72000 (d) ` 90000
18. If a/b = 3/4 and 8a + 5b=22, then the value of ‘a’ is [2012-I]
(a)1 (b) 1/2 (c) 3/2 (d) 3/4
19. If (a – b) is 6 more than (c + d) and (a + b) is 3 less than
(c – d), then the value of (a – c) is [2012-I]
(a) 0.5 (b) 1.0
(c) 1.5 (d) 2.0
20. The number whose square is equal to the difference of the
squares of 40 and 32 is [2012-II]
(a) 45.09 (b) 24
(c) 25 (d) 28
Number System/Simplification
21. 15 buckets of water fill a tank when the capacity of each
bucket is 7 litres How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 5 litres ?[2012-II]
(a) 12 (b) 24
(c) 21 (d) 30
22. A vessel, full of water, weighs 27.5 kg. when the vessel
is  1/4 full, it weighs 12.26 kg.  Find the weight of empty vessel
? [2012-II]
(a) 7.18 kg (b) 6.54 kg
(c) 2.75 kg (d) 2 5 kg
23. If a+b = 10 and ab = 21, find the value of a
3
+b
3
[2012-II]
(a) 370 (b) 210
(c) 730 (d) 598
24. If a/(a+b)=17/23, what is (a+b)/(a – b) equal to ? [2012-II]
(a) 13/7 (b) 23/11
(c) 14/5 (d) 25/9
25.
2
(598 479) (598 479)
(598 479)
2
+ --
´
[2012-II]
(a) 2 (b) 6
(c) 4 (d) 8
26. A jar contains b lack and white marbles. If there are ten marbles
in the jar, then which of the following could not be the ratio
of black to white marbles ? [2012-II]
(a) 9:1 (b) 7:3
(c) 1:10 (d) 6:4
27. The number whose square is equal to the difference of the
squares of 37 and 23 is [2013-I]
(a) 45.09 (b) 28.98
(c) 47.09 (d) 2 8
28. A vessel, full of water, weights 24 kg. When the vessel is
1/4 full, it weighs 9 kg. Find the weight of empty vessel.
[2013-I]
(a) 4 kg (b) 5 kg
(c) 8 kg (d) 3 kg
29. If a – b = 4 and ab = 45 find the value of a
3
 – b
3
. [2013-I]
(a) 6 04 (b) 370
(c) 2 53 (d) 199
30. If a/(a + b) = 15/21, what is (a + b)/(a – b) equal to ? [2013-I]
(a) 13/9 (b) 23/11
(c) 14/5 (d) 21/9
31.
( )( )
( )
22
798 579 798 579
798 579
+ --
´
 = ? [2013-I]
(a)2 (b) 6
(c)4 (d) 8
32. 18 buckets of water fill a tank when the capacity of each
bucket is 8 litres. How many buckets will be needed to fill the
same tank, if the capacity of the bucket is 12 litres ?[2013-I]
( a) 12
(b) 13.5
(c) 24
(d) can not be determined due to insufficient data
33. Find two natural numbers whose sum is 85 and the least
common multiple is 102. [2014-I]
(a) 30 and 55 (b) 17 and 68
(c) 35 and 55 (d) 51 and 34
34. In a fort there was sufficient food for 200 soldiers for 31
days. After 27 days, 120 soldiers left the fort. For how many
extra days will the rest of the food last for the remaining
soldiers ? [2014-I]
(a) 12 days (b) 10 days
(c) 8 days (d) 6 days
35. 10 is added to a certain number, the sum is multiplied
by 7, the product is divided by 5 and 5 is subtracted from
the quotient. The remainder left is half of 88. What is the
number ? [2014-I]
( a) 21 (b) 2 0 (c ) 25 (d) 3 0
36. A bag contains 25 paise, 50 paise and 1 ` coins. There are
220 coins in all and the total amount in the bag is ` 160. If
there are thrice as many 1 ` coins as there are 25 paise coins,
then what is the number of 50 paise coins ? [2014-I]
(a) 60 (b) 4 0 (c) 1 20 (d) 8 0
37. The sum of two numbers is equal to thrice their difference. If
the smaller of the numbers is 10 find the other number.
[2014-I]
( a) 15 (b) 3 0
(c) 40 (d) None of these.
 38. Simplify:
69 69 69 65 65 65
69 69 69 65 65 65
´ ´ - ´´
´ + ´+´
[2014-I]
(a)1 (b) 4
(c) 0.216 (d) 0.164
39. 7 is added to a certain number, the sum is multiplied by 5;
the product is divided by  9 and 3 is subtracted from the
quotient. The remainder left is 12. What is the number ?
[2014-II]
( a) 20 (b) 3 0
(c) 40 (d) 5
40. How many digits will be there to the right of the decimal
point in the product of  95.75 and 0.02554 ? [2014-II]
(a)5 (b) 6
(c)7 (d) Insufficient data
41. The average weight of 50 boys in a class is 45 kg. When one
boy leaves the class, the average reduces by 100g. Find the
weight of the boy who left the class. [2015-II]
(a) 50 kg. (b) 50.8 kg
(c) 49 kg (d) 49.9 kg
42. In Arun's opinion, his weight is greater than 65 kg but less
than 72 kg. His brother doest not agree with Arun and he
thinks that Arun's weight is greater than 60 kg but less than
70 kg. His mother's view is that his weight cannot be greater
than 68 kg. If all are them are correct in their estimation, what
is the average of different probable weights of Arun?
[2016-I]
(a) 67 kg (b) 68 kg
(c) 69 kg (d) data inadequate
Number System/Simplification
43. Present age of X and Y are in the ratio 7:5 respectively . Four
years hence, the ratio of their ages will become 11:9
respectively. What is the present age of Y? [2016-I]
(a) 1 year (b) 7 year
(c) 5 year (d) None of these
44. In an examination, a student was asked to find 
3
14
 of a
certain number. By mistake, he found 
3
4
of it. His answer
was 150 more than the correct answer. Find the number.
[2016 - II]
(a) 1 80 (b) 2 80
(c) 3 80 (d) 4 80
45. A crate of mangoes contains one bruised mango for every
30 mangoes in the crate. If 3 out of every 4 bruised mangoes
are considered unsalable, and there are 12 unsalable
mangoes in the crate, how many mangoes are there in the
crate? [2016 - II]
(a) 4 80 (b) 5 00
(c) 4 20 (d) 5 20
46. The mean of 50 observations was 36. It was found later that
an observation 48 was wrongly taken as 23. The corrected
new mean is [2016 - II]
(a) 35.2 (b) 34.1
(c) 36.5 (d) 39.1
47. The average score of a cricketer for ten matches is 38.9 runs.
If the average for the first six matches is 42, the average for
the last four matches is [2016 - II]
(a) 33.25 (b) 33.5
(c) 34.25 (d) 3 5
48. If A/B = 4/3 then what is the value of (9A–3B)/(9A+3B) is
[2017 - I]
(a) 3/5 (b) 5/3
(c) 2/5 (d) 3/7
49. If one student got 77/100, 96/150 and 103/350 in various
subjects, what is the percentage average? [2017 - I]
(a) 15.33% (b) 12.25%
(c)  16.33% (d) 18.15%
50. In an election between two candidates, Biku got 55% votes
of the total valid votes, 25% of the votes were declared
invalid. If total populations of the village were  6000. Find
the valid votes that Mahtre got, was [2017 - I]
(a) 1575 (b) 2025
(c) 2075 (d) 2175
51.  If 30% of a number is subtracted from 91 gives the same
number, find the number. [2017 - I]
(a) 80 (b) 9 0
(c) 70 (d) 6 0
52. If 50% of a number is added to 84 gives the same number,
what is the number? [2017 - I]
(a) 1 78 (b) 1 74
(c) 158 (d) 1 6 8
53. If 381A is divisible by 9, what is the least natural number A?
[2017 - I]
(a)6 (b) 1
(c)9 (d) 4
54. If a number exceeds 40% of itself by 56, then what is the
number? [2017 - II]
(a) 1 50 (b) 1 30
(c) 1 60 (d) 1 40
55. Average weight of 15 students increased by 1.5 kg when
one person of 40 kg is replaced by a new man. Then weight
of the new man is [2017 - II]
(a) 62.5 kg (b) 58.5 kg
(c) 72.5 kg (d) 54.5 kg
56. Average temperature of Tuesday to Thursday was 38 degree
celsius and that Wednesday to Friday was 37 degree celsius.
If the temperature on Friday was 39 degree celsius. The
temperature on Tuesday was? [2017 - II]
(a) 38 degree celsius (b) 36 degree celsius
(c) 42 degree celsius (d) 39 degree celsius
57. A men spend 1/3 of his income on food,1/4 of the rest on
rent and 1/5 of the rest on clothes. He still has Rs.1760 left
with him. Find his income? [2017 - II]
(a) 4400 (b) 4200
(c) 4800 (d) 5200
58. Two numbers are in the ratio 12 : 13. If 20 is subtracted from
each, the new numbers are in the ratio 2 : 3. The smaller
number is: [2017 - II]
(a) 26 (b) 2 4
(c) 32 (d) 2 8
59. The sum of two numbers is 36 and their H.C.F and L.C.M. are
3 and 105 respectively. The sum of the reciprocals of two
numbers is     [2018 - I]
(a)
2
35
(b)
3
25
(c)
4
35
(d)
2
25
60. A teacher wants to arrange his students in an equal number
of rows and columns. If there are 1369 students, the number
of students in the last row are     [2018 - I]
(a) 37 (b) 33 (c) 63 (d) 47
61. A farmer divides his herd of n cows among his four sons, so
that the first son gets one–half the herd, the second one–
fourth, the third son 
1
5
 and the fourth son 7 cows. Then the
value of n is     [2018 - I]
(a) 2 40 (b) 100 (c) 1 80 (d) 140
62. The average of 5/16 and 3/8 is__?             [2018 - II]
(a) 0.5425 (b) 0.2585
(c) 0.3475 (d) 0.4385
63. Find the value of  
0.0081
 + 
0.0064
 ?           [2018 - II]
(a) 0.27 (b) 0.7
(c) 0.17 (d) 0.4
Number System/Simplification
64. Find the value of  216
0.16
 × 16
0.18
 ?              [2018 - II]
(a)4 (b) 6
(c)8 (d) 2
65. If 
(a 8) (2a 1)
3 27
++
=
, then find 'a'?             [2018 - II]
(a)1 (b) 0
(c) –1 (d) 0.5
66. If 
2
 = 1.4142, find the value of
11
222
2 2 22
+++
+-
[2019-I]
(a) 1.4144 (b) 2.8284
(c) 28.284 (d) 2.4142
67. In an examination, a student was asked to find 
3
14
 of a certain
number. By mistake, he found 
3
4
of it. His answer was 150
more than the correct answer. Find the number. [2019 - II]
(a) 1 80 (b) 2 80
(c) 3 80 (d) 4 80
68.
5 6 83 31 7
? 1 32
67 9 54 3 9
¸´ - ¸ +´ = [2019 - II]
(a)
7
6
(b)
6
7
(c)1 (d) None of these
69. The whole number which is a multiple of every number is
[2019 - II]
(a)0
(b) 1
(c) There is no such number
(d) None of these
70. Highest common factor of 42 and 162 is ___. [2019 - II]
(a)6 (b) 4
(c) 12 (d) 2
71. The ratio betw een two numb ers is 3 : 4. If each numb er is increased
by 6 the ratio becomes 4 : 5. The diff erence betw een the numbers is
[2019 - II]
(a)1 (b) 3
(c)6 (d) 8
72. If A = x% of y and B = y% of x, then which of the following
is true? [2020 - I]
(a) A is smaller than B.
(b) A is greater than B
(c) None of these
(d) If x is smaller than y , then A is greater than B.
73. If 20% of A = B, then B% of 20 is the same as: [2020 - I]
(a) 4% of A (b) 5% of A
(c) 20% of A (d) None of these
74. The sum of ages of 5 children born at the intervals of 3 years
each is 50 years. What is the age of the youngest child?
[2020 - I]
(a) 4 years (b) 5 years
(c) 8 years (d) 10 years
75. The average weight of 8 person’s increases by 2.5 kg when
a new person comes in place of one of them weighing 65 kg.
What might be the weight of the new person? [2020 - I]
(a) 76kg (b) 76.5kg
(c) 85kg (d) Data inadequate
76. Present ages of Sameer and Anand are in the ratio of 5 : 4
respectively. Three years hence, the ratio of their ages will
become 11 : 9 respectively. What is Anand’s present age in
years? [2020 - I]
(a) 24 years (b) 27 years
(c) 40 years (d) Cannot be determined
77. What should come in place of both x in the equation
162
=
128
x
x
[2020 - I]
(a) 12 (b) 14
(c) 1 44 (d) 196
78. The value of 
0.1 0.1 0.1 0.02 0.02 0.02
0.2 0.2 0.2 0.04 0.04 0.04
´ ´ +´´
´ ´ +´´
 is?
[2020 - I]
(a) 0.0125 (b) 2 5
(c) 0.25 (d) 0.125
Number System/Simplification
ANSWERS & EXPLANATIONS
1. (d) Distance between two consecutive trees = 
222
25
= meters.
2. (b) According to question
R = 2S
S = 
1
G
5
    Þ  G = 5S
R + S + G = 1000
2S + S + 5S =  ` 1000
8S  = 1000
S = 125
Hence, Gagan’s get 5 × 125 =  ` 625.
3. (a) Let the number be x.
25x + 324 = 52x
52x – 25 x = 324
27x = 324
x = 12
4. (b) 365.089 –? + 89.72 = 302.35
? = 365.089 + 89.72 – 302.35
? = 152.459
5. (c) Let the number of girls be x.
60 × 3.60 + x × 2.40 = 312
x = 40
6. (c) Let the number of boys in class be x.
Therefore the number of girls in class be 5x.
Total number of children in class = x + 5x = 6x.
Hence, 35 cannot be the total number of children as it’s
not the multiple of 6.
7. (a) Let one variety of rice be x kg.
Another quantity = (50 – x) kg
According to question x × 4.50 + (50 – x) 5 = 240
4.5x + 250 – 5x = 240
0.5x = 10 ; x = 20
Hence, the quantity of cheaper rice was 20 kg.
8. (d) Let the number of each type of notes be x. According
to question 1 ×  x + 5 × x + 10 × x = 640
16x = 640 ; x = 40
Total number of notes = 40 + 40 + 40 = 120
9. (d) Let hens and cows are x and y respectively
x + y = 48 ....(1)
2x + 4y = 140
x + 2y = 70 ....(2)
After solving eq. (1) & (2)
y = 22
\ x = 26
10. (a) Let the number = x
According to question
3x = 29.7 x = 9.9
Correct answer = 
9.9
3.3
3
=
11. (d)
9
0.692;
13
=
17
0.654
26
=
28
0.717;
39
=
 
33
0.634
52
=
Hence, 
33
52
 is the smallest fraction.
12. (c)
2
0.67
3
=
3
0.6
5
=
7
0.7
9
=
9
0.81
11
=
8
0.88
9
=
Correct ascending order 
3 2 798
=
5 3 9 119
< < <<
13. (c) 337.62 + 8.591 + 34.4  = 380.611
14. (c)
1 1 11
9 6 12 72
+ ++ 
8 12 61
72
+ ++
Þ 
273
728
Þ=
15. (b) ? % of 932 + 30 = 309.6
? % of 932  = 309.6 – 30
                  
?
932 279.6
100
? 30.
´=
=
16. (b) Let the number = x
According to question
                 
2
x x 510
5
3x
510
5
510 5
x
3
x 850
10
10% of x 850 85
100
-=
=
´
=
=
= ´=
17. (a) Let estate cost is ` x
4
16800
5
x ´=
 ; x = 21000
V alue of 
3
21000 9000
7
´= = ` 9000
18. (c)
34
43
a
ba
b
= Þ=
8a + 5b = 22
4
8 5 22
3
aa +´=
24 20
3
+ aa
 = 22
44a = 66