Comparing Quantities
Class 7th Mathematics CBSE Solution
- Find ratio of: (a) Rs. 5 to 50 paise (b) 15 kg to 210 g (c) 9 m to 27 cm (d) 30…
- In a computer lab, there are 3 computers for every 6 students. How many…
- Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs. Area of…
- Convert the given fractional numbers to percent: (a) 1/8 (b) 5/4 (c) 3/40 (d)…
- Convert the given decimal fractions to per cents: (a) 0.65 (b) 2.1 (c) 0.02 (d)…
- Estimate what part of the figures is colored and hence find the per cent which…
- Find: (a) 15% of 250 (b) 1% of 1 hour (c) 20% of Rs. 2500 (d) 75% of 1 kg…
- Find the whole quantity if: (a) 5% of it is 600. (b) 12% of it is Rs. 1080. (c)…
- Convert given per cents to decimal fractions and also to fractions in simplest…
- In a city, 30% are females, 40% are males and remaining are children. What per…
- Out of 15,000 voters in a constituency, 60% voted. Find the percentage of voters…
- Meeta saves Rs 4000 from her salary. If this is 10% of her salary. What is her…
- A local cricket team played 20 matches in one season. It won 25% of them. How…
- Tell what is the profit or loss in the following transactions. Also find profit…
- Convert each part of the ratio to percentage:(a) 3:1(b) 2:3:5(c) 1:4(d) 1:2:5…
- The population of a city decreased from 25,000 to 24,500. Find the percentage…
- Arun bought a car for Rs. 3, 50, 000. The next year, the price went up to Rs.…
- I buy a T.V. for Rs. 10,000 and sell it at a profit of 20%. How much money do I…
- Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain. What…
- Chalk contains calcium, carbon and oxygen in the ratio 10: 3: 12. Find the…
- If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?…
- Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she…
- Find the amount to be paid at the end of 3 years in each case: (a) Principal =…
- What rate gives Rs. 280 as interest on a sum of Rs. 56,000 in 2 years?…
- If Meena gives an interest of Rs. 45 for one year at 9% rate p.a. What is the…
Exercise 8.1
Question 1.Find ratio of:
(a) Rs. 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Answer:
(a) We need to find the ratio of Rs 5 to 50 paise
We know that,
1 Rupee = 100 paise
Therefore,
5 Rupees = 500 Paise
Hence,
Ratio = 
= 
= 
Therefore,
Required ratio = 10: 1 Ans.
(b) We need to find the ratio of 15 kg to 210 g
We know that,
1 kg = 1000 g
Therefore,
15 kg = 15000 g
Hence,
Ratio = 
= 
= 
Therefore,
Required ratio = 500: 7 Ans.
(c) We need to find the ratio of 9 m to 27 cm
We know that,
1 m = 100 cm
Therefore,
9 m = 900 cm
Hence,
Required ratio = 
= 
= 
Therefore,
Required ratio = 100: 3 Ans.
(d) We need to find the ratio of 30 days to 36 hours
We know that,
1 day = 24 hours
Therefore,
30 days = 30 × 24
= 720 hours
Hence,
Required ratio = 
= 
= 
Therefore,
Required ratio = 20: 1 Ans.
Question 2.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Answer:
According to the question,
Number of computers required for 6 students = 3
Number of computers required for 1 student = 
Hence,
Number of computers required for 24 students = 
× 24
= 12
Ans: 12 computers are required for 24 students
Question 3.
Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs. Area of Rajasthan = 3 lakh km2 and area of UP = 2 lakh km2.
(i) How many people are there per km2 in both these States?
(ii) Which State is less populated?
Answer:
(i) According to the question,
Population of Rajasthan = 570 lakhs
Population of U.P = 1660 lakhs
Also, area of Rajasthan = 3 lakh km2
And, area of U.P = 2 lakh km2
Now,
Population of Rajasthan in 3 km2 area = 570 lakh
Population of Rajasthan in 1 km2 area = 
= 190 lakh
Also,
Population of U.P in 2 km2 area = 1660 lakh
Population of U.P in 1 km2 area = 
= 840 lakh
(ii) From the above results, it can be observed that,
Population of Rajasthan in 1 km2 area = 190 lakh
Population of U.P in 1 km2 area = 840 lakh
Therefore,
Population of Rajasthan per km2 area is lesser than that of U.P
Hence, Rajasthan is less populated.
Exercise 8.2
Question 1.Convert the given fractional numbers to percent:
(a) 
(b) 
(c) 
(d) 
Answer:
To convert a fraction into per cent, multiply the fraction by 100.
Therefore,
(a) 1/81/8 in percent = 1/8 × 100
= 1/8 × 100%
= 12.5 %
Hence, 1/8 = 12.5%(b)
5/4 in percent = 5/4 × 100
= 5/4 × 100%
= 5 × 25 %
= 125 %
Hence, 5/4 = 125%(c)
3/40 in percent = 3/40 × 100
= 3/40 × 100%
= 7.5 %
Hence, 3/40 = 7.5%(d)
2/7 = 2/7 × 100
= 2/7 × 100%
= 200/7 %
Converting the fraction in mixed fraction, we get,
= 
%
Question 2.
Convert the given decimal fractions to per cents:
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Answer:
(a) We need to convert 0.65 into percent
Therefore,
0.65 = 0.65 × 100 %
= 
%
= 65 %
(b) We need to convert 2.1 into percent
Therefore,
2.1 = 2.1 × 100 %
= 
%
= 210 %
(c) We need to convert 0.02 into percent
Therefore,
0.02 = 0.02 × 100 %
= 
%
= 2 %
(d) We need to convert 12.35 into percent
Therefore,
12.35 = 12.35 × 100 %
= 
%
= 1235 %
Question 3.
Estimate what part of the figures is colored and hence find the per cent which is colored.
(i) 
(ii) 
(iii) 
Answer:
(i) Here, we have:
Out of 4 equal parts, 1 part is shaded
Therefore,
It represents the fraction 
So, in form of percent,
= × 100 %
= 25%
(ii) Here, we have:
Out of 5 equal parts, 3 parts is shaded
Therefore,
It represents the fraction 
So, in form of percent,
= × 100 %
= 60%
(iii) Here, we have:
Out of 8 equal parts, 3 parts is shaded
Therefore,
It represents the fraction 
So, in form of percent,
= × 100 %
= 
%
= 37.5 %
Question 4.
Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of Rs. 2500
(d) 75% of 1 kg
Answer:
(a) We need to find 15 % of 250
Therefore,
15 % of 250 = 
× 250
= 
= 37.5
(b) We need to find 1% of 1 hour
We know that,
1 hour = 60 minutes
Therefore,
1 % of 1 hour = 1 % of 60 minutes
= 
× 60
= minutes
(c) We need to find 20% of Rs 2500
20 % of Rs 2500
Therefore,
20 % of Rs 2500 = 
× 2500
= 2 × 250
= Rs 500
(d) We need to find 75% of 1Kg
Therefore,
75 % of 1 kg = 
× 1
= 0.75 kg
We know that,
1 kg = 1000 g
Hence,
0.75 kg = (0.75 × 1000) g
= 750 g
Question 5.
Find the whole quantity if:
(a) 5% of it is 600.
(b) 12% of it is Rs. 1080.
(c) 40% of it is 500 km.
(d) 70% of it is 14 minutes.
(e) 8% of it is 40 liters.
Answer:
(a) 5% of it is 600.
Let the quantity be x
Therefore,
5 % of x = 600
5 % × x = 600
× x = 600
x = 600 × 
= 120 × 100
= 12000
Thus, the quantity is 12,000
(b) 12% of it is Rs. 1080.
Let the quantity be x
Therefore,
12 % of x = 1080
12 % × x = 1080
× x = 1080
x = 1080 × 
= 90 × 100
= Rs 9000
Thus, the quantity is Rs 9,000
(c) 40% of it is 500 km.
Let the quantity be x
Therefore,
40 % of x = 500
40 % × x = 500
× x = 500
x = 500 × 
= 12.5 × 100
= 1250 km
Thus, the quantity is 1250 km
(d) 70% of it is 14 minutes.
Let us assume the quantity to be x
Therefore,
70 % of x = 14
= 70 % × x = 14
= 
× x = 14
x = 14 × 
= 2 × 10
= 20 min
Thus, the quantity is 20 min
(e) 8% of it is 40 liters.
Let us assume the quantity to be x
Therefore,
8 % of x = 40
= 8 % × x = 40
= 
× x = 40
x = 40 × 
= 5 × 100
= 500 L
Thus, the quantity is 500 L
Question 6.
Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Answer:
(a) We have,
We have to convert 25% into decimal and also into fractions in simplest form
Now,
25 % = 
= (simple fraction form)
= 0.25 (decimal form)
(b) We have to convert 150% into decimal and also into fractions in simplest form
Now,
150 % = 
= 
= 
(simple fraction form)
= 1.5 (decimal form)
(c) We have to convert 20% into decimal and also into fractions in simplest form
Now,
20 % =
= 
(simple fraction form)
= 0.20 (decimal form)
(d) We have to convert 5% into decimal and also into fractions in simplest form
Now,
5 % =
= 
(simple fraction form)
= 0.05 (decimal form)
Question 7.
In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Answer:
It is given in the question that,
Percentage of Females = 30%
Percentage of Males = 40%
Therefore,
Percentage of Children = 100 - ( 30 + 40 ) %
= (100 – 70) %
= 30 %
Question 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:
It is given in the question that,
Total number of voters = 15,000
Percentage of voters who voted in the elections = 60 %
Percentage of voters who did not vote = (100 – 60) %
= 40 %
Hence,
Number of people who did not vote in the election = 40 % of Total number of voters
= × 
= 40 × 150
= 6000
Question 9.
Meeta saves Rs 4000 from her salary. If this is 10% of her salary. What is her salary?
Answer:
Let us assume the salary of Meeta be x
Savings of Meeta from her salary = Rs 4000
According to question:
10 % of x = Rs 4000
10 % × x = 4000
× x = 4000
= 4000
x = 4000 × 10
= Rs 40000
Therefore,
Salary of Meeta = Rs 40000
Question 10.
A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Answer:
According to the question:
Total number of matches played by a local cricket team in one season = 20
According to the question,
Number of matches won = 25 % of the total number of matches played by the team
= 25 % of 20
= × 20
= × 20
= 5
Hence,
Number of matches won by the team = 5
Exercise 8.3
Question 1.Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case
(a) Gardening shears bought for Rs. 250 and sold for Rs. 325.
(b) A refrigerator bought for Rs. 12,000 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) Gardening shears bought for Rs. 250 and sold for Rs. 325.
It is given in the question that,
Cost price of the product, CP = Rs 250
Selling price of the product, SP = Rs 325
Therefore,
Profit = Selling Price – Cost Price
= 325 – 250
= Rs 75
Also,
Profit % = 
× 100
= 
× 100
= 
× 4
= 7.5 × 4
= 30 %
(b) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500. It is given in the question that,
Cost price of the refrigerator, CP = Rs 12,000
Also,
Selling price of the refrigerator, SP = Rs 13,500
Therefore,
Profit = Selling Price – Cost Price
= 13,500 – 12,000
= Rs 1500
We know that,
Profit % = × 100
= 
× 100
= 
= 
= 12.5 %
(c)A cupboard bought for Rs. 2,500 and sold at Rs. 3,000.
It is given in the question that,
Cost price of the cupboard, CP = Rs 2500
Selling price of the cupboard, SP = Rs 3000
Profit = Selling Price – Cost Price
= 3000 – 2500
= Rs 500
Also,
Profit % = × 100
= 
× 100
= 
= 20 %
(d) A skirt bought for Rs. 250 and sold at Rs. 150.
It is given in the question that,
Cost price of the skirt, CP = Rs 250
Selling price of the skirt, SP = Rs 150
Therefore,
Loss = Cost Price – Selling Price
= 250 – 150
= Rs 100
Also,
Loss % = 
× 100
= 
× 100
= 
× 4
= 
= 40 %
Question 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) We have to convert 3:1 into percentage:
So, Total parts = 3 + 1 = 4
Therefore,
First part = 3/4× 100 %
= 75 %
And,
Second part = 1/4 × 100 %
= 25 %
(b) We have to convert 2: 3: 5 into percentage:
So,
Total parts = 2 + 3 + 5 = 10
Therefore,
First part = 2/10 × 100 %
= 20 %
And,
Second part = 3/10 × 100 %
= 30 %
Also,
Third part = 5/10 × 100 %
= 50 %
(c) We have to convert 1: 4 into percentage:
So,
Total parts = 1 + 4 = 5
Therefore,
First part = 1/5 × 100 %
= 20 %
And,
Second part = 4/5 × 100 %
= 80 %
(d) We have to convert 1:2: 5 into percentage:
So,
Total parts = 1 + 2 + 5 = 8
Therefore,
First part = 1/8 × 100 %
= 12.5 %
And,
Second part = 2/8 × 100 %
= 1/4 × 100 %
= 25 %
Also,
Third part = 5/8 × 100 %
= 62.5 %
Question 3.
The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Answer:
According to the question,
Initial population of the city = 25000
After the decrement in the population,
Final population of the city = 24500
Thus, the decrement in the population = 25000 – 24500
= 500
Hence,
Decrease percentage = 
× 100 %
= 
× 100
= 
× 100
= 2 %
Question 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:
According to the question,
Initial price of the car = Rs 3, 50, 000
After the increment in the price of the car,
Final price of the car = Rs 3, 70, 000
Therefore,
Increment in the price = 3, 70, 000 – 3, 50, 000
= Rs 20,000
Hence,
= 
× 100 %
= 
× 100 %
= 
%
= 5 
%
Question 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:
It is given in the question that,
Cost price of T.V, CP = Rs 10,000
Also,
Profit % = 20%
Now,
We know that,
Profit = 
× Cost Price
= × 10000
= × 10000
= Rs 2000
Also, we know that, Selling Price = Cost Price + Profit
Therefore,
Selling Price = 10, 000 + 2, 000
Selling Price = Rs. 12, 000
Hence, The person gets Rs 12000 for the T.V.
Question 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:
According to the question,
Selling price of washing machine,
SP = Rs 13, 500
Also, Loss % = 20 %
Let us assume the cost price of the machine be x
Therefore,
Loss = 20 % of x
loss =
x
Hence,
Cost price – Loss = Selling price
x – 
× x = 13500
x – x = 13500
x = 13500
x = 13500 × 
= 3375 × 5
= Rs 16875
Therefore, the cost price of the washing machine is Rs. 16875.
Question 7.
Chalk contains calcium, carbon and oxygen in the ratio 10: 3: 12. Find the percentage of carbon in chalk.
Answer:
It is given in the question that,
The ratio of calcium, carbon, and oxygen = 10: 3: 12
Therefore,
Total = 10 + 3 + 12 = 25
Hence,
Percentage of carbon = 
× 100 %
= 3 × 4 %
= 12 %
Question 8.
If in a stick of chalk, carbon is 3 g, what is the weight of the chalk stick?
Answer:
Let us assume the weight of the stick be x g
Also, the weight of carbon = 3 g
Therefore,
As carbon is 12% of the chalk,According to the question:
12 % of x = 3
Hence,
× x = 3
x = 3 ×
= 25 g
Thus, the weight of the chalk stick is 25 g.
Question 9.
Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it for?
Answer:
According to the question,
Cost price of the book = Rs 275
Also,
Loss % = 15 %
Let us assume the selling price of the book be x
Therefore,
Loss = 15 % of 275
= (15/100)275
Hence,
Cost price – Loss = Selling price
x = 275 – × 275
= 275 – 
= 275 – 41.25
= Rs 233.75
Thus, the selling price of the book be Rs 233.75
Question 10.
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) According to the question,
Principal (P) = Rs 1200
Rate (R) = 12 % p.a.
Time (T) = 3 years
We know that,
Simple interest (S.I) = 
Therefore,
S.I = 
= 12 × 12 × 3
= 144 × 3
= Rs 432
Hence,
Amount = Principal + S.I
= 1200 + 432
= Rs 1632
(b) According to the question,
Principal (P) = Rs 7500
Rate (R) = 5 % p.a.
Time (T) = 3 years
We know that,
Simple interest (S.I) =
Therefore,
S.I = 
= 75 × 5 × 3
= 75 × 15
= Rs 1125
Hence,
Amount = Principal + S.I
= 7500 + 1125
= Rs 8625
Question 11.
What rate gives Rs. 280 as interest on a sum of Rs. 56,000 in 2 years?
Answer:
According to the question,
Principal (P) = Rs 56,000
Time (T) = 2 years
S.I = Rs 280
We know that,
Simple interest (S.I) =
Therefore,
280 = 
28000 = 56000 × R × 2
R = 
= 
= 0.25 %
Hence, 0.25 % gives Rs 280 as a interest on the given sum.
Question 12.
If Meena gives an interest of Rs. 45 for one year at 9% rate p.a. What is the sum she has borrowed?
Answer:
It is given that,
Rate (R) = 9 % p.a.
Time (T) = 1 years
S.I = Rs 45
We know that,
Simple interest (S.I) =
Therefore,
45 = 
So, P = 
= Rs 500
Hence,
She borrowed Rs 500