Mental Maths Questions and Answers: Comparing Quantities | Mental Math for Class 7 PDF Download

 Page 1


 
  
 
 
Comparing  Quantities 
  
Points to remember: 
 
?  When two quantities of same kind are in the same units are 
compared by Division, ratio of two quantities is obtained. 
? A ratio has no unit. 
? A ratio is said to be in simplest form, if its two terms have no common 
factor other than one.  
? Comparison of two ratios is done by making them fractions with 
equal denominators and these ratios are called equivalent or 
proportional.   
? Another method of comparison is percentage.  
? Any simple fraction, decimal fraction or ratio can be converted into 
percentage and any percentage can be converted into simple fraction, 
decimal or ratio. 
Percentage means 'for each 100’; % = 
?? ??????
  
? When S.P. > C.P., there is profit. 
? Profit = S.P. - C.P.  
? Profit % = 
???????????? ?? .?? .
 × 100 %  
? When C.P > S.P, there is loss  
? Loss = C.P - S.P  
? Loss % = 
???????? ?? .?? .
× 100 %  
Page 2


 
  
 
 
Comparing  Quantities 
  
Points to remember: 
 
?  When two quantities of same kind are in the same units are 
compared by Division, ratio of two quantities is obtained. 
? A ratio has no unit. 
? A ratio is said to be in simplest form, if its two terms have no common 
factor other than one.  
? Comparison of two ratios is done by making them fractions with 
equal denominators and these ratios are called equivalent or 
proportional.   
? Another method of comparison is percentage.  
? Any simple fraction, decimal fraction or ratio can be converted into 
percentage and any percentage can be converted into simple fraction, 
decimal or ratio. 
Percentage means 'for each 100’; % = 
?? ??????
  
? When S.P. > C.P., there is profit. 
? Profit = S.P. - C.P.  
? Profit % = 
???????????? ?? .?? .
 × 100 %  
? When C.P > S.P, there is loss  
? Loss = C.P - S.P  
? Loss % = 
???????? ?? .?? .
× 100 %  
 
  
 
? Simple Interest =  
??????????????????  × ???????? ???? ????????????????  × ???????? ??????
 
TRICKS  
? A number which, when added to terms of a:b makes it equal to the 
c:d is 
???? -????
?? -?? 
  
? A number which, when subtracted from the terms of ratio a:b makes 
it equal to ratio c:d is 
???? -????
?? -?? 
  
? If the sum of two numbers is A and their difference is B, then the 
ratio of numbers is given by A + B : A – B  
? If a : b :: c : d, then a × d = b × c. 
 
Questions 
 
1. Find the ratio  
(a) `4 to 20 paisa    (b) 5 kg to 100 gram  
2.  Convert into percent:  
(a)  
?? ????
              (b)  
?? ????
             (c) 
?? ??  
3. Convert into fraction:  
(a)  62.5 %              (b)  72 %                (c)  28 %  
4. Find:  
(a)  15 % of `500                (b) 75 % of 180 kg  
5. Find x if:  
(a)  25 : 8 = x : 24               (b)  20 : x = 4 : 35  
6. Two amount of money are proportional to 5: 7. If the first is `20, then 
what is the other amount?  
Page 3


 
  
 
 
Comparing  Quantities 
  
Points to remember: 
 
?  When two quantities of same kind are in the same units are 
compared by Division, ratio of two quantities is obtained. 
? A ratio has no unit. 
? A ratio is said to be in simplest form, if its two terms have no common 
factor other than one.  
? Comparison of two ratios is done by making them fractions with 
equal denominators and these ratios are called equivalent or 
proportional.   
? Another method of comparison is percentage.  
? Any simple fraction, decimal fraction or ratio can be converted into 
percentage and any percentage can be converted into simple fraction, 
decimal or ratio. 
Percentage means 'for each 100’; % = 
?? ??????
  
? When S.P. > C.P., there is profit. 
? Profit = S.P. - C.P.  
? Profit % = 
???????????? ?? .?? .
 × 100 %  
? When C.P > S.P, there is loss  
? Loss = C.P - S.P  
? Loss % = 
???????? ?? .?? .
× 100 %  
 
  
 
? Simple Interest =  
??????????????????  × ???????? ???? ????????????????  × ???????? ??????
 
TRICKS  
? A number which, when added to terms of a:b makes it equal to the 
c:d is 
???? -????
?? -?? 
  
? A number which, when subtracted from the terms of ratio a:b makes 
it equal to ratio c:d is 
???? -????
?? -?? 
  
? If the sum of two numbers is A and their difference is B, then the 
ratio of numbers is given by A + B : A – B  
? If a : b :: c : d, then a × d = b × c. 
 
Questions 
 
1. Find the ratio  
(a) `4 to 20 paisa    (b) 5 kg to 100 gram  
2.  Convert into percent:  
(a)  
?? ????
              (b)  
?? ????
             (c) 
?? ??  
3. Convert into fraction:  
(a)  62.5 %              (b)  72 %                (c)  28 %  
4. Find:  
(a)  15 % of `500                (b) 75 % of 180 kg  
5. Find x if:  
(a)  25 : 8 = x : 24               (b)  20 : x = 4 : 35  
6. Two amount of money are proportional to 5: 7. If the first is `20, then 
what is the other amount?  
 
  
 
7. If 80 % students of a class of 45 students like to play cricket, then how 
many students don’t like to play cricket?  
8. Express the ratio of 12 cm to 25 cm in percentage.  
9. Express the ratio of `2 to `10 as a percentage.  
10. If CP of 16 articles is equal to SP of 20 articles, then find the gain or 
loss percent.  
11. 12.5 % more is gained by selling a pen for `88 instead of selling for 
`80. Find the CP of pen.  
12. A dishonest dealer decides to sell his goods at cost price but uses a 
weight of 800 gram for 1 kg weight. Find his gain percent.  
13. A sum of money amounts to `1000 in 3 years at a certain rate of 
interest and it amounts to `1200 in 4 years at same rate. Find the sum.  
14. At a certain rate of simple interest a certain sum doubles itself in 6 
years. In how many years will it triple itself?  
15. A shopkeeper marks his goods at 20 % above cost price but allows 10 
% discount for cash. What is his net profit percent?  
16. In what time period will `3000 triples itself, if the rate of interest is 
20 % per annum?  
17. A fruit basket has 20 apples out of which 30% are rotten.  How many 
good apples are there in the basket?     
18. A team won 8 games this year against 5 games won last year. What is 
the percentage increase this year?  
19. Sides of two squares are 7.5 cm and 5 cm respectively. Find the ratio 
of their areas.  
20. Manas saves 35 % from his salary. If his savings is `14000, then what 
is his salary?  
Page 4


 
  
 
 
Comparing  Quantities 
  
Points to remember: 
 
?  When two quantities of same kind are in the same units are 
compared by Division, ratio of two quantities is obtained. 
? A ratio has no unit. 
? A ratio is said to be in simplest form, if its two terms have no common 
factor other than one.  
? Comparison of two ratios is done by making them fractions with 
equal denominators and these ratios are called equivalent or 
proportional.   
? Another method of comparison is percentage.  
? Any simple fraction, decimal fraction or ratio can be converted into 
percentage and any percentage can be converted into simple fraction, 
decimal or ratio. 
Percentage means 'for each 100’; % = 
?? ??????
  
? When S.P. > C.P., there is profit. 
? Profit = S.P. - C.P.  
? Profit % = 
???????????? ?? .?? .
 × 100 %  
? When C.P > S.P, there is loss  
? Loss = C.P - S.P  
? Loss % = 
???????? ?? .?? .
× 100 %  
 
  
 
? Simple Interest =  
??????????????????  × ???????? ???? ????????????????  × ???????? ??????
 
TRICKS  
? A number which, when added to terms of a:b makes it equal to the 
c:d is 
???? -????
?? -?? 
  
? A number which, when subtracted from the terms of ratio a:b makes 
it equal to ratio c:d is 
???? -????
?? -?? 
  
? If the sum of two numbers is A and their difference is B, then the 
ratio of numbers is given by A + B : A – B  
? If a : b :: c : d, then a × d = b × c. 
 
Questions 
 
1. Find the ratio  
(a) `4 to 20 paisa    (b) 5 kg to 100 gram  
2.  Convert into percent:  
(a)  
?? ????
              (b)  
?? ????
             (c) 
?? ??  
3. Convert into fraction:  
(a)  62.5 %              (b)  72 %                (c)  28 %  
4. Find:  
(a)  15 % of `500                (b) 75 % of 180 kg  
5. Find x if:  
(a)  25 : 8 = x : 24               (b)  20 : x = 4 : 35  
6. Two amount of money are proportional to 5: 7. If the first is `20, then 
what is the other amount?  
 
  
 
7. If 80 % students of a class of 45 students like to play cricket, then how 
many students don’t like to play cricket?  
8. Express the ratio of 12 cm to 25 cm in percentage.  
9. Express the ratio of `2 to `10 as a percentage.  
10. If CP of 16 articles is equal to SP of 20 articles, then find the gain or 
loss percent.  
11. 12.5 % more is gained by selling a pen for `88 instead of selling for 
`80. Find the CP of pen.  
12. A dishonest dealer decides to sell his goods at cost price but uses a 
weight of 800 gram for 1 kg weight. Find his gain percent.  
13. A sum of money amounts to `1000 in 3 years at a certain rate of 
interest and it amounts to `1200 in 4 years at same rate. Find the sum.  
14. At a certain rate of simple interest a certain sum doubles itself in 6 
years. In how many years will it triple itself?  
15. A shopkeeper marks his goods at 20 % above cost price but allows 10 
% discount for cash. What is his net profit percent?  
16. In what time period will `3000 triples itself, if the rate of interest is 
20 % per annum?  
17. A fruit basket has 20 apples out of which 30% are rotten.  How many 
good apples are there in the basket?     
18. A team won 8 games this year against 5 games won last year. What is 
the percentage increase this year?  
19. Sides of two squares are 7.5 cm and 5 cm respectively. Find the ratio 
of their areas.  
20. Manas saves 35 % from his salary. If his savings is `14000, then what 
is his salary?  
 
  
 
21. Ankur saves 30 % from his salary. If his salary is `50000, then find 
his expenditure.  
22. If price of one dozen banana is `72, then find price of 15 such 
bananas.  
23. Ram purchased an old car for `100000. He spent 10 % of cost price 
on its repair. He sold the car for `99000, find his gain or loss percent.  
24. Iqbal purchased an old scooter for `20000 and spent 20 % of its CP 
on painting and sold the scooter for `30000. Find his gain or loss 
percent.  
25. If 30 % of y is 150, then find y.  
26. If 15 % of x is 60, then find x.  
27. A farmer gained 50 % after selling his cow for `15000. Find CP of 
the cow.  
28. A person sold his motorcycle for `38000 with 5 % loss, find CP of the 
motorcycle.  
29. Convert the ratio given below into percentage:  
(a)  2 : 3     (b)  3 : 5  
30. A sum of money triples itself in 25 years. Find the rate of interest.  
31. A sum of `2000 invested for 3 years at 6 % per annum. Find the 
amount at the end of 3rd year.  
32. A sum of `5000 invested for six months at 10 % per annum. Find the 
amount at the end of this time period.  
33. A sum doubles itself in 10 years. Find rate of interest.  
34. 3 kg of flour is enough for 15 people. How much flour is needed for 
such 80 people?  
35. A dealer buys a radio for `2500 and spends `500 on transportation. 
He sells the radio for `3300. Find his gain or loss percent. 
Page 5


 
  
 
 
Comparing  Quantities 
  
Points to remember: 
 
?  When two quantities of same kind are in the same units are 
compared by Division, ratio of two quantities is obtained. 
? A ratio has no unit. 
? A ratio is said to be in simplest form, if its two terms have no common 
factor other than one.  
? Comparison of two ratios is done by making them fractions with 
equal denominators and these ratios are called equivalent or 
proportional.   
? Another method of comparison is percentage.  
? Any simple fraction, decimal fraction or ratio can be converted into 
percentage and any percentage can be converted into simple fraction, 
decimal or ratio. 
Percentage means 'for each 100’; % = 
?? ??????
  
? When S.P. > C.P., there is profit. 
? Profit = S.P. - C.P.  
? Profit % = 
???????????? ?? .?? .
 × 100 %  
? When C.P > S.P, there is loss  
? Loss = C.P - S.P  
? Loss % = 
???????? ?? .?? .
× 100 %  
 
  
 
? Simple Interest =  
??????????????????  × ???????? ???? ????????????????  × ???????? ??????
 
TRICKS  
? A number which, when added to terms of a:b makes it equal to the 
c:d is 
???? -????
?? -?? 
  
? A number which, when subtracted from the terms of ratio a:b makes 
it equal to ratio c:d is 
???? -????
?? -?? 
  
? If the sum of two numbers is A and their difference is B, then the 
ratio of numbers is given by A + B : A – B  
? If a : b :: c : d, then a × d = b × c. 
 
Questions 
 
1. Find the ratio  
(a) `4 to 20 paisa    (b) 5 kg to 100 gram  
2.  Convert into percent:  
(a)  
?? ????
              (b)  
?? ????
             (c) 
?? ??  
3. Convert into fraction:  
(a)  62.5 %              (b)  72 %                (c)  28 %  
4. Find:  
(a)  15 % of `500                (b) 75 % of 180 kg  
5. Find x if:  
(a)  25 : 8 = x : 24               (b)  20 : x = 4 : 35  
6. Two amount of money are proportional to 5: 7. If the first is `20, then 
what is the other amount?  
 
  
 
7. If 80 % students of a class of 45 students like to play cricket, then how 
many students don’t like to play cricket?  
8. Express the ratio of 12 cm to 25 cm in percentage.  
9. Express the ratio of `2 to `10 as a percentage.  
10. If CP of 16 articles is equal to SP of 20 articles, then find the gain or 
loss percent.  
11. 12.5 % more is gained by selling a pen for `88 instead of selling for 
`80. Find the CP of pen.  
12. A dishonest dealer decides to sell his goods at cost price but uses a 
weight of 800 gram for 1 kg weight. Find his gain percent.  
13. A sum of money amounts to `1000 in 3 years at a certain rate of 
interest and it amounts to `1200 in 4 years at same rate. Find the sum.  
14. At a certain rate of simple interest a certain sum doubles itself in 6 
years. In how many years will it triple itself?  
15. A shopkeeper marks his goods at 20 % above cost price but allows 10 
% discount for cash. What is his net profit percent?  
16. In what time period will `3000 triples itself, if the rate of interest is 
20 % per annum?  
17. A fruit basket has 20 apples out of which 30% are rotten.  How many 
good apples are there in the basket?     
18. A team won 8 games this year against 5 games won last year. What is 
the percentage increase this year?  
19. Sides of two squares are 7.5 cm and 5 cm respectively. Find the ratio 
of their areas.  
20. Manas saves 35 % from his salary. If his savings is `14000, then what 
is his salary?  
 
  
 
21. Ankur saves 30 % from his salary. If his salary is `50000, then find 
his expenditure.  
22. If price of one dozen banana is `72, then find price of 15 such 
bananas.  
23. Ram purchased an old car for `100000. He spent 10 % of cost price 
on its repair. He sold the car for `99000, find his gain or loss percent.  
24. Iqbal purchased an old scooter for `20000 and spent 20 % of its CP 
on painting and sold the scooter for `30000. Find his gain or loss 
percent.  
25. If 30 % of y is 150, then find y.  
26. If 15 % of x is 60, then find x.  
27. A farmer gained 50 % after selling his cow for `15000. Find CP of 
the cow.  
28. A person sold his motorcycle for `38000 with 5 % loss, find CP of the 
motorcycle.  
29. Convert the ratio given below into percentage:  
(a)  2 : 3     (b)  3 : 5  
30. A sum of money triples itself in 25 years. Find the rate of interest.  
31. A sum of `2000 invested for 3 years at 6 % per annum. Find the 
amount at the end of 3rd year.  
32. A sum of `5000 invested for six months at 10 % per annum. Find the 
amount at the end of this time period.  
33. A sum doubles itself in 10 years. Find rate of interest.  
34. 3 kg of flour is enough for 15 people. How much flour is needed for 
such 80 people?  
35. A dealer buys a radio for `2500 and spends `500 on transportation. 
He sells the radio for `3300. Find his gain or loss percent. 
 
  
 
36. At what rate percent per annum will `8000 amounts to `10000 in a 
year?  
37. 15 persons finish a work in 30 days, how many days will be taken to 
finish the same work by 5 persons?   
38. The first three numbers of a proportion are 8, 10 and 12. Find the 
fourth number.  
39. The ratio of three angles of a triangle is 3:4:5. Find the smallest angle.  
40. Ratio of calcium, carbon and oxygen in chalk is 8: 3: 9. Find the 
percentage of carbon in the chalk.  
41. A library contains 50 % of books in Hindi, 30 % of books in English 
and remaining 300 books are in Punjabi. Find total number of books 
in library.  
42. The population of a town has increased from 80000 to 92000. Find 
the percentage increase in population.  
43. There are 12 boys and 8 girls in a class. Find the percentage of girls 
in the class.  
44. What percentage of 5 km is 200 meter?  
45. Annual income of a person is `800000. If his salary increases 5 % per 
annum, what will be his salary after 2 years?  
46. What is the ratio of 6 minutes to 1 hour?  
47. If 3 : x :: 9 : 15 find x.  
48. 70 % of a number is 28. Find the number.  
49. If ratio of the cost price and selling price of an article is 5 : 6, then 
find the gain or loss percent.  
50. A man buys balloons at the rate of 3 balloons for a rupee and sells 
them at the rate of 2 balloons for a rupee. Find his gain or loss 
percent.