NCERT Solutions for Chapter 8 Comparing Quantities Class 7 Maths
Book Solutions1
Find the 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
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 [∵ 1 kg = 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 [ ∵ 1 m = 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
Exercise 8.1
Page Number 157
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 needed = 3 computers
Therefore 1 student needs = 3/6 computers
24 students needs = 3/6times 24 = 12 computers
Thus, 12 computers will be needed for 24 students.
Exercise 8.1
Page Number 157
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 km2= 190 people per km2
In U.P. = 1660 lakhs/2 lakh km2= 830 people per km2
(ii) Rajasthan is less populated.
Exercise 8.1
Page Number 157
1
Convert the given fractional numbers to percent:
(a) 1/8
(b) 5/4
(c) 3/40
(d) 2/7
Answer
(a) 1/8 = 1/8×100%=25/2% = 12.5%
(b) 5/4 = 5/4×100% = 5 x 25% = 125%
(c) 3/40 = 3/40×100%=3/2×5%=15/2% = 7.5%
(d) 2/7=2/7×100%=200/7%=28.4/7%
Exercise 8.2
Page Number 164
2
Convert the given decimal fractions to percents:
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Answer
(a) 0.65 = 65/100×100% = 65%
(b) 2.1 = 21/10×100%= 210%
(c) 0.02 = 2/100×100% = 2%
(d) 12.35 = 1235/100×100% = 1235%
Exercise 8.2
Page Number 165
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 = 1/4×100% = 25%
(ii) Coloured part = 3/5
∴ Percent of coloured part = 3/5×100% = 60%
(iii) Coloured part = 3/8
∴ Percent of coloured part = 3/8×100% = 3/2×25%
= 37.5%
Exercise 8.2
Page Number 165
4
Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of Rs. 2500
(d) 75% of 1 kg
Answer
(a) 15% of 250 = 15/100×250= 15 x 2.5 = 37.5
(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60) seconds
= 1/100×60×60 = 6 x 6 = 36 seconds
(c) 20% of Rs. 2500 = 20/100×2500 = 20 x 25 = Rs. 500
(d) 75% of 1 kg = 75% of 1000 g = 75/100×1000 = 750 g = 0.750 kg
Exercise 8.2
Page Number 165
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
Let the whole quantity be x in given questions:
(a) 5% of x = 600
⇒ 5/100× x=600
⇒ x=600×100/5 = 12,000
(b) 12% of x = Rs. 1080
⇒12/100 × x=1080
⇒ x=1080×100/12x = Rs. 9,000
(c) 40% of x = 500 km
⇒ 40/100 × x=500
⇒ x=500×100/40x = 1,250 km
(d) 70% of x = 14 minutes
⇒ 70/100 × x=14
⇒ x=14×100/70x= 20 minutes
(e) 8% of x = 40 liters
⇒ 8/100 × x=40
⇒ x=40×100/8x = 500 liters
Exercise 8.2
Page Number 165
6
Convert given percents 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 |
Exercise 8.2
Page Number 165
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.
Exercise 8.2
Page Number 165
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 = 40/100×15000= 6,000
Hence, 6,000 candidates did not vote.
Exercise 8.2
Page Number 165
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
⇒ 10/100 × x=400
⇒ x=400×100/10
⇒ x= 4,000
Hence, Meera’s salary is Rs. 4,000.
Exercise 8.2
Page Number 165
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 = 25/100×20 = 5
Hence, they won 5 matches.
Exercise 8.2
Page Number 165
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 for Rs. 12,000 and sold for Rs. 13,500.
(c) A cupboard bought for Rs. 2,500 and sold for Rs. 3,000.
(d) A skirt bought for Rs. 250 and sold for 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. = 325 – 250 = Rs. 75
Now Profit% = Profit/C.P.×100 = 75/250×100 = 30%
Therefore, Profit = Rs. 75 and Profit% = 30%
(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. = 13500 – 12000 = Rs. 1,500
Now Profit% = Profit/C.P.×100 = 1500/12000×100 = 12.5%
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. – C.P. = 3,000 – 2,500 = Rs. 500
Now Profit% = Profit/C.P.×100 = 500/2500×100 = 20%
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 = C.P. – S.P. = 250 – 150 = Rs. 100
Now Loss% = Loss/C.P.×100 = 100/250×100 = 40%
Therefore, Profit = Rs. 100 and Profit% = 40%
Exercise 8.3
Page Number 171
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 = 34:1434:14
⇒ Percentage of parts = 34×100:14×100
⇒ Percentage of parts = 75% : 25%
(b) 2 : 3 : 5
Total part = 2 + 3 + 5 = 10
Therefore, Fractional part = 210:310:510
⇒ Percentage of parts = 210×100:310×100:510×100
⇒ Percentage of parts = 20% : 30% : 50%
(c) 1 : 4
Total part = 1 + 4 = 5
Therefore, Fractional part = 15:45
⇒ Percentage of parts = 15×100:45×100
⇒ Percentage of parts = 20% : 80%
(d) 1 : 2 : 5
Total part = 1 + 2 + 5 = 8
Therefore, Fractional part = 18:28:58
⇒ Percentage of parts = 18×100:28×100:58×100
⇒ Percentage of parts = 12.5% : 25% : 62.5%
Exercise 8.3
Page Number 171
3
The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Answer
The population of a city decreased from 25,000 to 24,500.
Population decreased = 25,000 – 24,500 = 500
Decreased Percentage = Population decreased/Original population×100
= 500/25000×100 = 2%
Hence, the percentage decreased is 2%.
Exercise 8.3
Page Number 171
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 = Amount of change/Original amount×100
= 20000/350000×100 = 557%
Hence, the percentage of price increased is 557%.
Exercise 8.3
Page Number 171
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.
= 20/100×10000 = Rs. 2,000
Selling price = C.P. + Profit
= 10,000 + 2,000 = Rs. 12,000
Hence, he gets Rs. 12,000 on selling his T.V.
Exercise 8.3
Page Number 171
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.
⇒ Loss = 20% of Rs.x = 20/100 × x=x/5
Therefore, S.P. = C.P. – Loss
⇒ 13500 = x−x/5 ⇒ 13500 = 4x/5
⇒ x=13500×5/4x = Rs. 16,875
Hence, the cost price of washing machine is Rs. 16,875.
Exercise 8.3
Page Number 171
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 = 3/25×100 = 12%
(ii) Quantity of Carbon in chalk stick = 3 g
Let the weight of chalk be x g.
Then, 12% of x = 3
⇒ 12/100 × x =3
⇒ x=3×100/12 = 25 g
Hence, the weight of chalk stick is 25 g.
Exercise 8.3
Page Number 171
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 price of a book = Rs. 275
Loss percent = 15%
Loss = Loss% of C.P. = 15% of Rs. 275 = 15/100×275 = Rs. 41.25
Therefore, S.P. = C.P. – Loss = 275 – 41.25 = Rs. 233.75
Hence, Amina sells a book for Rs. 233.75.
Exercise 8.3
Page Number 172
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
Simple Interest = (P × R × T)/100 = (1200×12×3)/100 = Rs. 432
Now, Amount = Principal + Simple Interest = 1200 + 432 = Rs. 1,632
(b) Here, Principal (P) = Rs. 7,500, Rate (R) = 5% p.a., Time (T) = 3 years
Simple Interest = (P × R × T)/100 = (7500×5×3)/100 = Rs. 1,125
Now, Amount = Principal + Simple Interest = 7,500 + 1,125 = Rs. 8,625
Exercise 8.3
Page Number 172
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
Simple Interest = (P × R × T)/100
⇒ 280 = (56000×R×2)/100
⇒ R = (280×100/(56000×2)
⇒ R = 0.25%
Hence, the rate of interest on sum is 0.25%.
Exercise 8.3
Page Number 172
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 year
Simple Interest = P × R × T100P × R × T100
⇒ 45 = (P×9×1)/100
⇒ P = (45×100)/(9×1)
⇒ P = Rs. 500
Hence, she borrowed Rs. 500.
Exercise 8.3
Page Number 172