The chapter starts by explaining Equivalent Ratios.
- Two ratios can be compared by converting them to like fractions. If the two fractions are equal, we say the two given ratios are equivalent.
- Keeping things in proportion and getting solutions: If two ratios are equivalent then the four quantities are said to be in proportion. For example, the ratios 8 : 2 and 16 : 4 are equivalent therefore 8, 2, 16 and 4 are in proportion.
A way of comparing quantities is percentage.
Percentages are numerators of fractions with denominator 100.
- Meaning of Percentage
- Percentages when total is not hundred
- Converting Fractional Numbers to Percentage
- Converting Decimals to Percentage
- Converting Percentages to Fractions or Decimals
- Fun with Estimation
Percentages are widely used in our daily life:
- To find exact number when a certain percent of the total quantity is given.
- When parts of a quantity are given to us as ratios, it is seen how to convert them to percentages.
- The increase or decrease in a certain quantity can also be expressed as percentage.
- The profit or loss incurred in a certain transaction can be expressed in terms of percentages.
- While computing interest on an amount borrowed, the rate of interest is given in terms of percents.
- Interpreting Percentages
- Converting Percentages to “How Many”
- Ratios to Percents
- Increase or Decrease as Per Cent
- Profit or Loss as a Percentage
Amount = Principal + Interest.
- The money you borrow is known as sum borrowed or principal.
- Keeping this money for some time the borrower has to pay some extra money to the bank. This is known as Interest.
- Interest for Multiple Years
This is a very important chapter not only from the examination point of view but also in handling the day to day life purchases.
All the important points of the discussion are summarized at the end of the chapter- Comparing Quantities.
Page No 157:
Question 1:
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:
(a) Rs 5 to 50 paise
1 rupee = 100 paise
5 rupee = 500 paise
Hence, the required ratio is 10:1.
(b) 15 kg to 210 g
1 kg = 1000 g
15 kg = 15000 g
Hence, the required ratio is 500:7.
(c) 9 m to 27 cm
1 m = 100 cm
9 m = 900 cm
Hence, the required ratio is 100:3.
(d) 30 days to 36 hours
1 days = 24 hrs
30 days = 24 × 30 = 720 hrs
Hence, the required ratio is 20:1.
Page No 157:
Question 2:
In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?
Answer:
For 6 students, number of computers required = 3
∴
For 1 student, number of computers required =
∴
For 24 students, number of computers required ==
12
Hence, 12 computers are required for 24 students.
Page No 157:
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) Population of Rajasthan in 3 km2 area = 570 lakh
Population of Rajasthan in 1 km2 area =
Population of U.P in 2 km2 area = 1660 lakh
Population of U.P in 1 km2 area = = 830 lakh
(ii) It can be observed that population per km2 area is lesser for Rajasthan. Therefore, Rajasthan is less populated.
Video Solution for comparing quantities (Page: 157 , Q.No.: 3)
NCERT Solution for Class 7 math - comparing quantities 157 , Question 3
Page No 164:
Question 1:
Convert the given fractional numbers to per cents.
(a) (b)
(c) (d)
Answer:
(a)
(b)
(c)
(d)
Page No 165:
Question 2:
Convert the given decimal fractions to per cents.
(a) 0.65 (b) 2.1 (c) 0.02 (d) 12.35
Answer:
(a) 0.65
(b)2.1
(c) 0.02
(d) 12.35
Page No 165:
Question 3:
Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Answer:
(i) Here,
1 part out of 4 equal parts are shaded which represents the fraction
.
(ii) Here,
3 parts out of 5 equal parts are shaded which represents the fraction
.
(iii) Here,
3 parts out of 8 equal parts are shaded which represents the
fraction.
Page No 165:
Question 4:
Find:
(a) 15% of 250 (b) 1% of 1 hour
(c) 20% of Rs 2500 (d) 75% of 1 kg
Answer:
(a)
(b) 1 hour = 60 minutes
(c)
(d)
Page No 165:
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
Answer:
(a) 5% of x = 600
(b) 12% of x = Rs 1080
(c) 40% of x = 500 km
(d) 70% of x = 14 min
(e) 8% of x = 40 L
= 500 L
Page No 165:
Question 6:
Convert given percents to decimal fractions and also to fractions in simplest forms:
(a) 25% (b) 150%
(c) 20% (d) 5%
Answer:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Page No 165:
Question 7:
In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Answer:
It is given that 30% are females and 40% are males.
Children = (100 − 30 − 40) % = 30%
Page No 165:
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:
Percentage of voters who voted = 60%
Percentage of those who did not vote = 100% − 60% = 40%
Number of people who did not vote = 40% of 15000
Therefore, 6000 people did not vote.
Video Solution for comparing quantities (Page: 165 , Q.No.: 8)
NCERT Solution for Class 7 math - comparing quantities 165 , Question 8
Page No 165:
Question 9:
Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?
Answer:
Let Meeta’s salary be Rs x.
Given that,
10% of x = 400
x = 400 × 10 = Rs 4000
Therefore, Meeta’s salary is Rs 4000.
Page No 165:
Question 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 games won = 25% of 20
Therefore, the team won 5 matches.
Page No 171:
Question 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 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 = Rs 250
Selling price = Rs 325
Profit = 325 − 250 = Rs 75
==
30%
(b) Cost price = Rs 12000
Selling price = Rs 13,500
Profit = 13500 − 12000 = Rs 1500
Profit % =
= 12.5%
(c) Cost price = Rs 2500
Selling price = Rs 3000
Profit = 3000 − 2500 = Rs 500
Profit % ==
20%
(d) Cost price = Rs 250
Selling price = Rs 150
Loss = 250 − 150 = Rs 100
Loss % =
= 40%
Page No 171:
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) 3: 1
Total parts = 3 + 1 = 4
1st
part
2nd
part =
(b) 2: 3: 5
Total parts = 2 + 3 + 5 = 10
1st
part =
2nd
part =
3rd
part =
(c) 1: 4
Total parts =1 + 4 = 5
1st
part =
2nd
part =
(d) 1: 2: 5
Total parts = 1 + 2 + 5 = 8
1st
part =
2nd
part =
3rd
=
Page No 171:
Question 3:
The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Answer:
Initial population = 25000
Final population = 24500
Decrease = 500
% decrease
=
Page No 171:
Question 4:
Arun bought a car for Rs 3,50,000. The next year, the price went upto
Rs 3,70,000. What was the percentage of price increase?
Answer:
Initial price = Rs 350000
Final price = Rs 370000
Increase = Rs 20000
% increase
=
=
%
Page No 171:
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:
Cost price = Rs 10000
Profit = 20% of 10000
= Rs 2000
Selling price = Cost price + Profit
= 10000 + 2000 = Rs 12,000
Video Solution for comparing quantities (Page: 171 , Q.No.: 5)
NCERT Solution for Class 7 math - comparing quantities 171 , Question 5
Page No 171:
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:
Selling price = Rs 13500
Loss % = 20%
Let the cost price be x.
∴ Loss = 20% of x
Cost price − Loss = Selling price
= 16875
Therefore, she bought it for Rs 16875.
Video Solution for comparing quantities (Page: 171 , Q.No.: 6)
NCERT Solution for Class 7 math - comparing quantities 171 , Question 6
Page No 171:
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 3g, what is the weight of the chalk stick?
Answer:
(i) Ratio of calcium, carbon, and oxygen = 10: 3: 12
As 10 + 3 +12 = 25,
Therefore, percentage of carbon =
= 12%
(ii) Let the weight of the stick be x g.
12 % of x = 3
Page No 172:
Question 8:
Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?
Answer:
Cost price = Rs 275
Loss % = 15%
Loss = 15% of 275
Cost price − Loss = Selling price
275 − 41.25 = Selling price
Selling price = Rs 233.75
Page No 172:
Question 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) Principal (P) = Rs 1200
Rate (R) = 12 % p.a.
Time (T) = 3 years
= Rs 432
Amount = P + S.I.
= 1200 + 432
= Rs 1632
(b) P = Rs 7500
R = 5% p.a.
T = 3 years
= Rs 1125
Amount = 7500 + 1125
= Rs 8625
Page No 172:
Question 10:
What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?
Answer:
Therefore, 0.25% gives Rs 280 as interest on the given sum.
Page No 172:
Question 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:
= Rs 500
Therefore, she borrowed Rs 500.
Video Solution for comparing quantities (Page: 172 , Q.No.: 11)
NCERT Solution for Class 7 math - comparing quantities 172 , Question 11
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