NCERT Solutions for Class 7 Maths Ch 8 Comparing Quantities

Chapter 8 Comparing Quantities Class 7 NCERT Solutions of Maths is very helpful in preparing yourself well in the examinations.  These NCERT Solutions are prepared by Studyrankers experts which are detailed and accurate so you can always check whenever in doubt. It will guide students in a better way which will make student confident.

NCERT Solutions for Class 7 Maths Ch 8 Comparing Quantities

Exercise 8.1

1. Find the ratio of:
(a) Rs5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours

Answer

To find ratios, both quantities should be in same unit.

(a) Rs 5 to 50 paise
⇒ 5 x 100 paise to 50 paise [∴ Rs 1 = 100 paise]
⇒ 500 paise to 50 paise
Thus, the ratio is = 500/50 = 10/1 = 10 : 1

(b) 15 kg to 210 g
⇒ 15 x 1000 g to 210 g [∵ 1kg = 1000 g]
⇒ 15000 g to 210 g
Thus, the ratio is = 15000/210 = 500/7 = 500:7

(c) 9 m to 27 cm
⇒ 9 x 100 cm to 27 cm [∵ 1m = 100 cm]
⇒ 900 cm to 27 cm
Thus, the ratio is = 900/27 = 100/3 = 100:3

(d) 30 days to 36 hours
⇒ 30 x 24 hours to 36 hours [∵ 1 day = 24 hours]
⇒ 720 hours to 36 hours
Thus, the ratio is = 720/36 = 20/1 = 20:1

2. In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students? 

Answer

∵ 6 students need = 3 computers
∵ 1 student needs = 3/6 computers
∵ 24 students need = 
Thus, 12 computers will be needed for 24 students.

3. Population of Rajasthan = 570 lakhs and population of U.P. = 1660 lakhs. Area of Rajasthan = 3 lakh km2 and area of U.P. = 2 lakh km2
(i) How many people are there per km2 in both states? 
(ii) Which state is less populated? 

Answer

(i) People present per km2 = Population/Area
In Rajasthan = 570 lakhs/3 lakhs per km2 = 190 people km2
In UP = 1660 lakhs/2 lakhs per km2 = 830 people per km2

(ii) Rajasthan is less populated.

Exercise 8.2

1. Convert the given fractional numbers to percent: 
(a) 1/8
(b) 5/4
(c) 3/40
(d) 2/7

Answer


2. Convert the given decimal fractions to per cents: 
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35

Answer


3. Estimate what part of the figures is coloured and hence find the percent which is coloured.
Answer

(i) Coloured part = 1/4
∴ Percent of coloured part 
(ii) Coloured part = 3/5
∴ Percent of coloured part 
(iii) Coloured part = 3/8
∴ Percent of coloured part = 37.5%

4. Find: 
(a) 15% of 250 
(b) 1% of 1 hour 
(c) 20% of 2500 
(d) 75% of 1 kg 

Answer
(a) 15% of 250 
(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60] seconds
(c) 20% of Rs 500 

5. Find the whole quantity if: 
(a) 5% of it is 600 
(b) 12% of it is ₹1080
(c) 40% of it is 500 km 
(d) 70% of it is 14 minutes 
(e) 8% of it is 40 litres

Answer

Let the whole quantity be x in given questions:

6. Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25% 
(b) 150% 
(c) 20% 
(d) 5% 

Answer

S. No.  Percents Fractions Simplest form Decimal form
(a) 25% 25/100 1/4 0.25
(b) 150% 150/100 3/2 1.5
(c) 20% 20/100 1/5 0.2
(d) 5% 5/100 1/20 0.05

7. In a city, 30% are females, 40% are males and remaining are children. What percent are children?

Answer

Given: Percentage of females =30%
Percentage of males = 40%
Total percentage of females and males = 30 + 40 = 70%
Percentage of children = Total percentage - Percentage of males and females
= 100%-70%
= 30%
Hence, 30% are children.

8. Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote? 

Answer

Total voters = 15,000
Percentage of voted candidates = 60%
Percentage of not voted candidates = 100 - 60 = 40%
Actual candidates, who did not vote = 40% of 15000 
Hence, 6,000 candidates did not vote.

9. Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?

Answer

Let Meera's salary be Rs x.
Now, 10% of salary = Rs 400
⇒ 10% of x = Rs 400
Hence, Meera's salary is Rs 4,000.

10. A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win? 

Answer

Number of matches played by cricket team = 20
Percentage of won matches = 25%
Total matches won by them = 25% of 20
= 5
Hence, they won 5 matches.

Exercise 8.3 

1. Tell what is the profit or loss in the following transactions. Also find profit percent or loss percent in each case. 
(a) Gardening shears bought for Rs 250 and sold for Rs 325. 
(b) A refrigerator bought Rs12,000 and sold at Rs 13,500. 
(c) A cupboard bought for Rs 2,500 and sold at Rs 3,000. 
(d) A skirt bought for Rs 250 and sold at Rs 150. 

Answer

(a) Cost price of gardening shears = Rs 250
Selling price of gardening shears = Rs 325
Since, S.P. > C.P., therefore here is profit.
∴ Profit = S.P. - C.P. = Rs 325 - Rs 250 = Rs 75 
Now,

(b) Cost price of refrigerator = Rs 12,000
Selling price of refrigerator = Rs 13,500
Since, S.P. > C.P., therefore here is profit.
∴ Profit = S.P. - C.P. = Rs 13500 - Rs 12000 = Rs 1,500
Now,
Therefore, Profit = Rs 1,500 and Profit% = 12.5%

(c) Cost price of cupboard = Rs 2,500
Selling price of cupboard = Rs 3,000
Since, S.P. > C.P., therefore here is profit.
∴ Profit = S.P. - CP. = Rs 3,000 - Rs 2,500 = Rs 500
Now,
Therefore, Profit = Rs 500 and Profit% = 20%

(d) Cost price of skirt = Rs 250
Selling price of skirt = Rs 150
Since, C.P. > S.P., therefore here is loss.
∴ Loss = CP, - S.P. = Rs 250 - Rs 150 = Rs100
Now,
Therefore, Profit = Rs 100 and Profit% = 40%

2. Convert each part of the ratio to percentage: 
(a) 3 : 1 
(b) 2 : 3 : 5 
(c) 1 : 4 
(d) 1 : 2 : 5 

Answer

(a) 3 :1 
Total part =3 + 1= 4
Therefore, Fractional part = 3/4 : 1/4
⇒ Percentage of parts 
⇒ Percentage of parts = 75% : 25%

(b) 2 : 3 : 5
Total part = 2 + 3 + 5 = 10
Therefore, Fractional part 

⇒ Percentage of parts 
⇒ Percentage of parts = 20% : 30% : 50%

(c) 1:4
Total part =1 + 4 = 5
Therefore, Fractional part = 1/5 : 4/5
⇒ Percentage of parts 
⇒ Percentage of parts = 20%: 00%

(d) 1 : 2 : 5
Total part = 1+ 2 + 5 = 8
Therefore, Fractional part 
⇒ Percentage of parts 
⇒ Percentage of parts = 12.5% : 25% : 62.5%

3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.

Answer

The decreased population of a city from 25,000 to 24,500.
Population decreased = 25,000 - 24,500 = 500
Decreased Percentage 
Hence, the percentage decreased is 2%.

4. Arun bought a car for Rs 3,50,000. The next year, the price went up to Rs 3,70,000. What was the percentage of price increase?

Answer

Increased in price of a car from Rs 3,50,000 to Rs 3,70,000.
Amount change = Rs 3,70,000 - Rs 3,50,000 = Rs 20,000.
Therefore, Increased percentage 
Hence, the percentage of price increased is 

5. I buy a T.V. for Rs 10,000 and sell it at a profit of 20%. How much money do I get for it?

Answer

The cost price of T.V. = Rs 10,000
Profit percent = 20% Now,
Profit = Profit% of C.P, 
Selling price = C.P. + Profit = Rs 10,000 + Rs 2,000 = Rs 12,000
Hence, he gets Rs 12,000 on selling his T.V.

6. Juhi sells a washing machine for Rs 13,500. She loses 20% in the bargain. What was the price at which she bought it? 

Answer

Selling price of washing machine = Rs. 13,500
Loss percent = 20%
Let the cost price of washing machine be Rs x.
Since, Loss = Loss% of C.P.
⇒ 
Therefore, S.P. = C.P, - Loss

7. (i) Chalk contains Calcium, Carbon and Oxygen in the ratio 10:3:12. Find the percentage of Carbon in chalk. 
(ii) If in a stick of chalk, Carbon is 3 g, what is the weight of the chalk stick?

Answer

(i) Given ratio = 10 : 3 : 12
Total part = 10 + 3 + 12 = 25 
Part of Carbon = 3/25
Percentage of Carbon part in chalk 

(ii) Quantity of Carbon in chalk stick = 3 g
Let the weight of chalk be x g.
Then, 12 % of x = 3
Hence, the weight of chalk stick is 25 g.

8. Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?

Answer

The cost of a book = Rs 275
Loss percent = 15%
Loss = Loss% of C.P. = 1 5 % of Rs 275
Therefore, S.P. = C.P. - Loss = Rs 275 - Rs 41.25 = Rs 233.75
Hence, Amina sells a book for Rs 233.75.

9. Find the amount to be paid at the end of 3 years in each case: 
(a) Principal = Rs 1,200 at 12% p.a. 
(b) Principal = Rs 7,500 at 5% p.a.

Answer

(a) Here, Principal (P) = Rs 1,200, Rate (R) = 12% p.a., Time (T) = 3 years
Now, Amount = Principal + Simple Interest
= Rs 1200 + Rs 432 
= Rs 1,632
(b) Here, Principal (P) = Rs 7,500, Rate (R) = 5% p.a., Time (T) = 3 years
Now, Amount = Principal + Simple Interest
= Rs 7,500 + Rs 1,125
= Rs 8,625

10. What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years? 

Answer

Here, Principal (P) = Rs 56,000, Simple Interest (S.I.) = Rs 280, Time (T) = 2 years
Hence, the rate of interest on sum is 0.25%.

11. If Meena gives an interest of Rs 45 for one year at 9% rate p.a. What is the sum she has borrowed?

Answer

Simple Interest = Rs 45, Rate (R) = 9% p.a., Time (T) = 1 years
Hence, she borrowed Rs 500.
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