NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities.
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.1
Question 1.
Find the ratio of:
(a) ₹ 5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hour
Solution:
(a) ₹ 5 : 50 paise
= ₹ 5 : 50 paise
= 5 × 100 paise : 50 paise
= 500 paise : 50 paise
= 10 : 1.
(b) 15 kg to 210g
= 15 kg : 210g
= 15 × 1000 g : 210g
= 15000 g : 210g = 500:7.
(c) 9 m to 27 cm
= 9m : 27 cm = 9 × 100 cm : 27 cm
= 900 cm : 27 cm
900 : 27 = 100 : 3.
(d) 30 days to 36 hours
= 30 days : 36 hours
30 × 24 hours : 36 hours
= 720 hours : 36 hours
= 720 : 36 = 20 : 1.
Question 2.
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Solution:
Let x computers be needed for 24 students.
Hence, 12 computers will be needed for
24 students.
Aliter :
∵ For every 6 students there are 3 computers
∴ For 1 student there are \(\frac { 3 }{ 6 } \) computer
∴ For 24 students there are \(\frac { 3 }{ 6 } \) × 24 computers = 12 computers
Hence, 12 computers are needed 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?
Solution:
(i) Number of people per sq. km. in Rajasthan state
(ii) The Rajasthan State is less populated
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.2
Question 1.
Convert the given fractional numbers to per cents.
(a) \(\frac { 1 }{ 8 } \)
(b) \(\frac { 5 }{ 4 } \)
(c) \(\frac { 3 }{ 40 } \)
(d) \(\frac { 2 }{ 7 } \)
Solution:
Question 2.
Convert the given decimal fractions to per cents.
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Solution:
Question 3.
Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Solution:
Question 4.
Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of ₹ 2500
(d) 75% of 1 kg.
Solution:
Question 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.
Solution:
Question 6.
Convert given percents to decimal fractions and also to fractions in simplest forms.
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Solution:
Question 7.
In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Solution:
[100% (30% + 40%)] are children
⇒ [100% – 70% ] are children
⇒ 30% are children.
Question 8.
Out of 15,000 voters in a consti-tuency, 60% voted. Find the percentage of voters who did not vote. Can you now find how many actually did not vote?
Solution:
100% – 60% = 40% did not vote. Number of voters who did not actually vote
= 40% of 15,000
= \(\frac { 40 }{ 100 } \) × 15000 = 6000.
Question 9.
Meeta saves ₹ 400 from her salary. If this is 10% of her salary. What is her salary?
Solution:
Let her salary be ₹ P. Then, 10% of P = 400
⇒ \(\frac { 10 }{ 100 } \) × p = 400 ⇒ \(\frac { P }{ 10 } \) = 400
⇒ P = 400 × 10
⇒ P = 4000
Hence, her salary is ₹ 4000.
Question 10.
A local cricket team played 20 matches in one season. It won 25% of them,. How many matches did they win?
Solution:
Let the total number of matches won be P. Then,
25% of 20 = P
⇒ \(\frac { 25 }{ 100 } \) × 20 = p ⇒ 5 = p
⇒ p = 5
Hence, they won 5 matches.
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities Ex 8.3
Question 1.
Tell what is the profit or loss in the following transactions. Also find profit percent or loss per cent in each case.
(a) Gardening shears bought for ₹ 250 and sold for ₹ 325.
(b) A refrigerater bought for ₹ 12,000 and sold at ₹ 13,500.
(c) Acupboard bought for ₹ 2,500 and sold at ₹ 3,000.
(d) A skirt bought for ₹ 250 and sold at ₹ 150.
Solution:
Question 2.
Convert each part of the ratio to percentage
(a) 3 : 1
(b) 2 : 3 : 5
(c) 1 : 4
(d) 1 : 2 : 5.
Solution:
Question 3.
The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Solution:
Question 4.
Arun bought a car for ₹ 3,50,000. The next year, the price went upto ₹ 3,70,000. What was the percentage of price increase?
Solution:
Question 5.
1 buy a T.V. for ₹ 10,000 and sell it at a profit of 20%. How much money do I get for it?
Solution:
C.P. = ₹ 10,000
Profit = 20% of C.P.
= 20% of ₹ 10,000
= ₹ \(\frac { 20 }{ 100 } \) × 10,000 = ₹ 2,000
∴ S.P. = C.P. + Profit
= ₹ 10,000 + ₹ 2,000 = ₹ 12,000
Hence, I get ₹ 12,000 for it.
Question 6.
Juki sells a washing machine for ₹ 13,500. She loses 20% in the bargain. What was the price at which she brought it?
Solution:
Question 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?
Solution:
Question 8.
Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?
Solution:
C.P. = ₹ 275
Loss = 15% of C.P = \(\frac { 15 }{ 100 } \) × C.P
= \(\frac { 15 }{ 100 } \) × 275 = ₹ 41.25
S.P. = C.P. – Loss
= 275 – 41.25 = ₹ 233.75
hence, she se11 it for ₹ 233.75.
Question 9.
Find the amount to be paid at the end of 3 years in each case :
(a) Principal = ₹ 1,200 at 12% p.a.
(b) Principal = ₹ 7,500 aat 5% p.a.
Solution:
Question 10.
What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?
Solution:
Question 11.
If Meena gives an interest of ₹ 45 for one year at 9% rate p.a. What is the sum she has borrowed?
Solution:
NCERT Solutions for Class 7 Maths Chapter 8 Comparing Quantities MCQ
Important Multiple Choice Questions
1. The ratio of ? 10 to 50 paise is
(a) 20 : 1
(b) 10 : 1
(c) 5 : 1
(d) 1 : 20.
2. The ratio of 6 kg to 400 g is
(a) 10 : 1
(b) 15 : 1
(c) 12 : 1
(d) 6 : 1.
3. The ratio of 3 m to 60 cm is
(a) 4 : 1
(b) 3 : 1
(c) 5 : 1
(d) 2 : 1.
4. The ratio of 15 days to 72 hours is
(a) 2 : 1
(b) 3 : 1
(c) 4 : 1
(d) 5 : 1.
5. The ages of father and son are 45 years and 10 years. The ratio of their ages is
(a) 3 : 2
(b) 5 : 2
(c) 9 : 2
(d) 15 : 2.
6. The cost of 3 envelopes is ₹ 15. Find the cost of 5 envelopes.
(a) ₹ 20
(b) ₹ 25
(c) ₹ 30
(d) ₹ 40.
7. The cost of 7 kg of potatoes is ₹ 42. How many kg of potatoes can be purchased for ₹ 96?
(a) 10 kg
(b) 12 kg
(c) 15 kg
(d) 16 kg.
8. The cost of 4 m of cloth is ? 40. Find the cost of 9 m of cloth.
(a) ₹ 90
(b) ₹ 60
(c) ₹ 50
(d) ₹ 40.
9. The cost of 8 pencils is ₹ 10. Find the cost of 20 pencils.
(a) ₹ 20
(b) ₹ 25
(c) ₹ 24
(d) ₹ 30.
10. A motorcycle goes 120 km in 3 l of petrol. How much petrol will be required to go 600 km?
(a) 10 l
(b) 12 l
(c) 15 l
(d) 20 l.
11. \(\frac { 1 }{ 4 } \) as per cent is
(a) 20%
(b) 25%
(c) 30%
(d) 12 \(\frac { 1 }{ 2 } \)%.
12. \(\frac { 1 }{ 8 } \) as per cent is
(a) 25%
(b) 121%
(c) 20%
(d) 16%.
13. \(\frac { 5 }{ 2 } \) as per cent is
(a) 125%
(b) 150%
(c) 200%
(d) 250%.
14. 0.1 as per cent is
(a) 1%
(b) 10%
(c) 100%
(d) 0.1%.
15. 0.04 as per cent is
(a) 10%
(b) 20%
(c) 25%
(d) 4%.
16. \(\frac { 2 }{ 2 } \) as per cent is
(a) 19%
(b) 10%
(c) 100%
(d) none of these.
17. Out of 40 children in a class, 10 are boys. What is the percentage of boys?
(a) 10%
(b) 40%
(c) 4%
(d) 25%.
18. Out of 25 students, 5 are absent. What per cent of the students are absent?
(a) 10%
(b) 20%
(c) 25%
(d) 30%.
19. A shop has 50 televisions, out of which 5 are defective, defective? What per cent are
(a) 5%
(b) 10%
(c) 50%
(d) 25%.
20. There are 100 voters. 50 of them votes yes. What per cent voted yes?
(a) 10%
(b) 25%
(c) 50%
(d) 15%.
21. If 40% of students in a class are Hindus, what per cent of the students are non – Hindus?
(a) 40%
(b) 10%
(c) 50%
(d) 60%.
22. A basket is full of bananas, mangoes and apples. If 50% are mangoes, 30% are apples, then what per cent are bananas?
(a) 10%
(b) 20%
(c) 25%
(d) 40%.
23. What is 5% of 200?
(a) 2
(b) 5
(c) 10
(d) 100.
24. What is 12 \(\frac { 1 }{ 2 } \) % of 200?
(a) 25
(b) 12
(c) 40
(d) 100.
25. There are 40 children in a class. 25% like playing football. How many children like playing football?
(a) 10
(b) 20
(c) 30
(d) 40.
26. The salary of Manish is ₹ 4000. He saves 10% of his salary. How much does he save?
(a) ₹ 400
(b) ₹ 2000
(c) ₹ 3000
(d) ₹ 4000.
27. Convert \(\frac { 1 }{ 5 } \) to per cent
(a) 10%
(b) 20%
(c) 40%
(d) 80%.
28. A traveller covered 8% of his total journey which is 50 km long on foot. How many kilometre did he cover on foot?
(a) 1 km
(b) 2 km
(c) 3 km
(d) 4 km.
29. In a particular kind of pulses, the quantity of protein is 25%. How much protein is there in 4 kg of that pulse?
(a) 1kg
(b) 2kg
(c) 3kg
(d) 4kg.
30. Meenu purchased a coat for 7 600. She had to pay 4% sales tax on it. Find the amount of sales tax.
(a) ₹ 24
(b) ₹ 16
(c) ₹ 20
(d) ₹ 32.
31. The price of petrol has risen from ₹ 48 to ₹ 52 a litre. By what per cent has the price risen up?
(a) \(\frac { 25 }{ 3 } \) % or 8.33%
(b) 25%
(c) 4%
(d) 40%.
32. ₹ 100 are to be divided between Apala and Meenu. Apala gets 60%. What does Meenu get?
(a) ₹ 10
(b) ₹ 20
(c) ₹ 30
(d) ₹ 40.
33. The angles of a triangle are in the ratio 1:1:2. What is the largest angle?
(a) 90°
(b) 45°
(c) 30°
(d) 60°.
34. The marks in a test decreased from 40 to 30. The percentage decrease is
(a) 10%
(b) 20%
(c) 25%
(d) 40%.
35. The number of students in 2008 was 1000. It became 1100 in 2009. The percentage increase is
(a) 10%
(b) 5%
(c) 100%
(d) 1000%.
36. An article was purchased for ₹ 100 and sold for ₹ 120. What is the profit?
(a) ₹ 20
(b) ₹ 100
(c) ₹ 120
(d) None of these.
37. A watch was purchased for ₹ 316 and sold for ₹ 300. What is the loss?
(a) ₹ 16
(b) ₹ 8
(c) ₹ 24
(d) ₹ 32.
38. A shopkeeper bought a table for ₹ 500 and sold it for ₹ 400. Find the loss percentage.
(a) 10%
(b) 20%
(c) 40%
(d) 50%.
39. Meenu purchased an item for ₹ 800 and sold the same for ₹ 1000. The gain percentage is
(a) 25%
(b) 20%
(c) 40%
(d) 50%.
40. The interest on a sum of ₹ 2500 for 4 years at the interest rate 4% is
(a) ₹ 100
(b) ₹ 200
(c) ₹ 300
(d) ₹ 400.
ANSWERS
HINTS/SOLUTIONS
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