Andhra Pradesh SCERT Class 7 Maths Comparing Quantities Question and Answers Solutions
Andhra Pradesh SCERT 7th Class Maths Solutions Chapter 7 Comparing Quantities Question and answers. Students who are searching for Andhra Pradesh Class 7 Maths Chapter 7 can find here Solution of this chapter.
Board |
Andhra Pradesh (AP Board) |
Class |
7th |
Subject |
Maths |
Topic |
Solution |
EXERCISE 7.1
1.) Convert the given fractional numbers to per cents.
(a) 1/8
ANSWER:
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
1/8 x 100/100
We know, 1/100 = %
1/8 x 100%
100% / 8
1/8 = 12.5%
(b) 5/4
ANSWER:
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
5/4 x 100/100
We know, 1/100 = %
5/4 x 100%
500% / 4
5/4 = 125%
(c) 3/40
ANSWER:
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
3/40 x 100/100
We know, 1/100 = %
3/40 x 100%
300% / 40
3/40 = 7.5%
(d) 2/7
ANSWER:
We multiply and divide by 100
2/7 x 100/100
We know, 1/100 = %
2/7 x 100%
200% / 7
2/7 = 28.5714%
2.) Convert the given decimal fractions to per cents.
(a) 0.65
ANSWER:
We have to convert given decimal fractions to per cents.
There are 2 decimal point in 0.65.
0.65 x 100%
65/100 x 100%
0.65 = 65%
(b) 2.1
ANSWER:
We have to convert given decimal fractions to per cents.
There are 1 decimal point in 2.1
2.1 x 100%
21/10 x 100%
2.1 = 210%
(c) 0.02
ANSWER:
We have to convert given decimal fractions to per cents.
There are 2 decimal point in 0.02
0.02 x 100%
2 /100 x 100%
0.02 = 2%
(d) 12.35
ANSWER:
We have to convert given decimal fractions to per cents.
There are 2 decimal point in 12.35
12.35 x 100%
1235 /100 x 100%
12.35 = 1235%
3.) Estimate what part of the figures is coloured and hence find the per cent which is coloured.
ANSWER:
We have to find what part of the figures is coloured.
Also we have to find the per cent which is coloured.
From given figure,
There are 4 part out of that 1 part is coloured.
Coloured part = 1/4
Now, we have to convert 1/4 into percent.
We multiply and divide by 100
1/4 x 100/100
We know, 1/100 = %
1/4 x 100%
100% / 4
1/4 = 25%
ANSWER:
We have to find what part of the figures is coloured.
Also we have to find the per cent which is coloured.
From given figure,
There are 5 part out of that 3 part is coloured.
Coloured part = 3/5
Now, we have to convert 3/5 into percent.
We multiply and divide by 100
3/5 x 100/100
We know, 1/100 = %
3/5 x 100%
300% / 5
3/5 = 60%
ANSWER:
We have to find what part of the figures is coloured.
Also we have to find the per cent which is coloured.
From given figure,
There are 8 part out of that 3 part is coloured.
Coloured part = 3/8
Now, we have to convert 3/8 into percent.
We multiply and divide by 100
3/8 x 100/100
We know, 1/100 = %
3/8 x 100%
300% / 8
3/5 = 37.5%
4.) Find:
(a) 15% of 250
ANSWER:
We have to find 15% of 250
We know,
% = 1/100
15% = 15/100
15% of 250 = 15/100 x 250
15% of 250 = (15 x 250) /100
15% of 250 = 37.5
(b) 1% of 1 hour
ANSWER:
We have to find 1% of 1 hour
We know,
1 hour = 60 minute = 3600 second
% = 1/100
1% = 1/100
1% of 1 hour = 1/100 x 1 hour or 60 minute
1% of 1 hour = 60 /100
1% of 1 hour = 3/5 or 36 seconds
(c) 20% of Rs.2500
ANSWER:
We have to find 20% of Rs.2500
We know,
% = 1/100
20% = 20/100
20% of Rs.2500 = 20/100 x 2500
20% of Rs.2500 = (20 x 2500) /100
20% of Rs.2500 =Rs.500
(d) 75% of 1 kg
ANSWER:
We have to find 75% of 1 kg
1 kg = 1000 gm.
We know,
% = 1/100
75% = 75/100
75% of 1 kg = 75/100 x 1000
75% of 1 kg = (75 x 1000) /100
75% of 1 kg =750 gm.
5.) Find the whole quantity if
(a) 5% of it is 600.
ANSWER:
We have to find whole quantity and given that 5% of it is 600.
We know,
% = 1/100
5% = 5/100
5/100 = 600
We have to find 100%
5% = 600
100% = ?
We do cross multiplication,
? = (600 x 100%) / 5%
? = 600 x 20
? = 12000
Whole quantity is 12000.
(b) 12% of it is Rs.1080.
ANSWER:
We have to find whole quantity and given that 12% of it is Rs.1080.
We know,
% = 1/100
12% = 12/100
12/100 = 1080
We have to find 100%
12% = 1080
100% = ?
We do cross multiplication,
? = (1080 x 100%) / 12%
? = 90 x 100
? = 9000
Whole quantity is 9000.
(c) 40% of it is 500 km.
ANSWER:
We have to find whole quantity and given that 40% of it is 500 km.
We know,
% = 1/100
40% = 40/100
40/100 = 500 km
We have to find 100%
40% = 500 km
100% = ?
We do cross multiplication,
? = (500 x 100%) / 40%
? = 500 x 2.5
? = 1250 km
Whole quantity is 1250 km.
(d) 70% of it is 14 minutes.
ANSWER:
We have to find whole quantity and given that 70% of it is 14 minutes.
We know,
% = 1/100
70% = 70/100
70/100 = 14 minutes.
We have to find 100%
70% = 14 minutes.
100% = ?
We do cross multiplication,
? = (14 x 100%) / 70%
? = 1400 / 70
? = 20 minutes.
Whole quantity is 20 minutes.
(e) 8% of it is 40 litres.
ANSWER:
We have to find whole quantity and given that 8% of it is 40 litres.
We know,
% = 1/100
8% = 8/100
8/100 = 40 litres.
We have to find 100%
8% = 40 litres.
100% = ?
We do cross multiplication,
? = (40 x 100%) / 8%
? = 5 x 100
? = 500 litres.
Whole quantity is 500 litres.
6.) Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
ANSWER:
We have to convert given per cents to decimal fractions and also we have to convert fractions in simplest forms.
25%
We know,
% = 1/100
25% = 25/100 = 0.25
We have to convert 25/100 in simplest forms.
25/100 = 1/4
(b) 150%
ANSWER:
We have to convert given per cents to decimal fractions and also we have to convert fractions in simplest forms.
150%
We know,
% = 1/100
150% = 150/100 = 1.50
We have to convert 150/100 in simplest forms.
150/100 = 3/2
(c) 20%
ANSWER:
We have to convert given per cents to decimal fractions and also we have to convert fractions in simplest forms.
20%
We know,
% = 1/100
20% = 20/100 = 0.20
We have to convert 20/100 in simplest forms.
20/100 = 1/5
(d) 5%
ANSWER:
We have to convert given per cents to decimal fractions and also we have to convert fractions in simplest forms.
5%
We know,
% = 1/100
5% = 5/100 = 0.05
We have to convert 5/100 in simplest forms.
5/100 = 1/20
7.) In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
ANSWER:
Given that,
In a city, 30% are females, 40% are males and remaining are children
We have to find per cent of children.
We know any data is always 100%
In that,
30% are females, 40% are males
100% = 30% + 40% + per cent of children
100% = 70% + per cent of children
Per cent of children = 100% – 70%
Per cent of children = 30%
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:
Given that,
Out of 15,000 voters in a constituency, 60% voted.
We have to find the percentage of voters who did not vote.
Also we have to find how many actually did not vote.
Total 15,000 voters in a constituency.
100% = 15,000 voters
60% voted.
Percentage of voters who did not vote = 100% – 60% voted.
Percentage of voters who did not vote = 40%
Now,
We find Voters who did not vote.
100% = 15,000 voters
40% =? Voters
We do cross multiplication.
? Voters = 15000 x 40 / 100
? Voters = 6000
6000 Voters who did not vote.
9.) Meeta saves Rs. 4000 from her salary. If this is 10% of her salary. What is her salary?
ANSWER:
Given that,
Meeta saves Rs. 4000 from her salary
This is 10% of her salary
We have to find her salary.
Meeta’s salary =
10% = Rs. 4000
100% = ?
We do cross multiplication.
? = 4000 x 100 / 10
? = Rs.40000
Meeta’s salary is Rs.40000.
10.) A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
ANSWER:
Given that,
A local cricket team played 20 matches in one season. It won 25% of them.
We have to find how many matches did they win.
We find 25% of 20 matches
25% x 20 matches
We know,
% = 1/100
25/100 x 20 matches
1/4 x 20
= 5 matches.
5 matches did they win.
EXERCISE 7.2
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.
ANSWER:
Given that,
Gardening shears bought for Rs. 250 and sold for Rs. 325
We know,
The buying price of any item is known as its cost price.
Cost price = Rs. 250
The price at which you sell is known as the selling price.
Selling price = Rs. 325
CP < SP, then we got profit
Profit = SP – CP.
Profit = Rs. 325 – Rs. 250
Profit = Rs. 75.
Now,
Percent Profit = (Profit / Cost price) x 100%
Percent Profit = (75/250) x 100%
Percent Profit = 30%
(b) A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.
ANSWER:
Given that,
A refrigerator bought for Rs. 12,000 and sold at Rs. 13,500.
We know,
The buying price of any item is known as its cost price.
Cost price = Rs. 12,000
The price at which you sell is known as the selling price.
Selling price = Rs. 13,500.
CP < SP, then we got profit
Profit = SP – CP.
Profit = Rs. 13,500 – Rs. 12000
Profit = Rs. 1500.
Now,
Percent Profit = (Profit / Cost price) x 100%
Percent Profit = (1500/12000) x 100%
Percent Profit = 12.5%
(c) A cupboard bought for Rs.2,500 and sold at Rs. 3,000.
ANSWER:
Given that,
A cupboard bought for Rs.2, 500 and sold at Rs. 3,000.
We know,
The buying price of any item is known as its cost price.
Cost price = Rs.2, 500
The price at which you sell is known as the selling price.
Selling price = Rs. 3,000.
CP < SP, then we got profit
Profit = SP – CP.
Profit = Rs. 3,000 – Rs. 2, 500
Profit = Rs. 500.
Now,
Percent Profit = (Profit / Cost price) x 100%
Percent Profit = (500/2500) x 100%
Percent Profit = 20%
(d) A skirt bought for Rs. 250 and sold at Rs. 150.
ANSWER:
Given that,
A skirt bought for Rs. 250 and sold at Rs. 150.
We know,
The buying price of any item is known as its cost price.
Cost price = Rs.250
The price at which you sell is known as the selling price.
Selling price = Rs.150.
CP > SP we got Loss.
Loss = CP – SP.
Loss = Rs.250 – Rs.150.
Loss = Rs.100.
Now,
Percent Loss = (Loss / Cost price) x 100%
Percent Loss = (100/250) x 100%
Percent Loss = 40%
2.) Convert each part of the ratio to percentage:
(a) 3 : 1
ANSWER:
We have convert each part of the ratio into percentage.
Total parts of ratio = 3 + 1 = 4
Now, we have to find 3 part out of 4 parts.
3/4
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
3/4 x 100/100
We know, 1/100 = %
3/4 x 100%
300% / 4
3/4 = 75%
Now,
We have to find 1 part out of 4 parts.
1/4
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
1/4 x 100/100
We know, 1/100 = %
1/4 x 100%
100% / 4
1/4 = 25%
(b) 2 : 3 : 5
ANSWER:
We have convert each part of the ratio into percentage.
Total parts of ratio = 2 + 3 + 5 = 10
Now, we have to find 2 part out of 10 parts.
2/10
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
2/10x 100/100
We know, 1/100 = %
2/10x 100%
200% / 10
2/10= 20%
Now,
We have to find 3 part out of 10 parts.
3/10
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
3/10 x 100/100
We know, 1/100 = %
3/10 x 100%
300% / 10
3/10 = 30%
Now,
We have to find 5 part out of 10 parts.
5/10
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
5/10 x 100/100
We know, 1/100 = %
5/10 x 100%
500% / 10
5/10 = 50%
(c) 1:4
ANSWER:
We have convert each part of the ratio into percentage.
Total parts of ratio = 1 + 4 = 5
Now, we have to find 1 part out of 5 parts.
1/5
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
1/5 x 100/100
We know, 1/100 = %
1/5 x 100%
100% / 5
1/5 = 20%
Now,
We have to find 4 part out of 5 parts.
4/5
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
4/5x 100/100
We know, 1/100 = %
4/5x 100%
400% / 5
4/5 = 80%
(d) 1 : 2 : 5
ANSWER:
We have convert each part of the ratio into percentage.
Total parts of ratio = 1 + 2 + 5 = 8
Now, we have to find 1 part out of 8 parts.
1/8
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
1/8x 100/100
We know, 1/100 = %
1/8x 100%
100% / 8
1/8= 12.5%
Now,
We have to find 2 part out of 8 parts.
2/8
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
2/8x 100/100
We know, 1/100 = %
2/8x 100%
200% / 8
2/8= 25%
Now,
We have to find 5 part out of 8 parts.
5/8
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
5/8 x 100/100
We know, 1/100 = %
5/8 x 100%
500% / 8
5/8 = 62.5%
3.) The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
ANSWER:
Given that,
The population of a city decreased from 25,000 to 24,500.
We have to find the percentage decrease.
We know,
The percentage decrease = (amount of change/ original amount) × 100
Amount of change = 25,000 – 24,500.
Amount of change = 500
The percentage decrease = (500/25000) × 100
The percentage decrease = 2%
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:
Given that,
Arun bought a car for Rs. 3, 50,000. The next year, the price went upto Rs. 3, 70,000.
We have to find the percentage increase.
We know,
The percentage increase= (amount of change/ original amount) × 100
Amount of change = Rs. 3, 70,000 – Rs. 3, 50,000.
Amount of change = Rs. 20,000
The percentage increase= (20000/350000) × 100
The percentage increase = 5(5/7)%
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:
Given that,
I buy a T.V. for Rs. 10,000 and sell it at a profit of 20%.
We have to find how much money I get for it.
We first find 20% profit on Rs. 10,000
20% x 10000
We know,
% = 1/100
20/100 x 10000
= 2000
20% profit is Rs. 2000
Money I get for it = Rs. 10,000 + Rs. 2000 = Rs. 12000
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:
Given that,
Juhi sells a washing machine for Rs. 13,500. She loses 20% in the bargain
We have to find what the price at which she bought it was.
We 1st find 20% loss on Rs. 13,500.
20% x Rs. 13,500.
We know,
% = 1/100
20/100 x Rs. 13,500.
= Rs. 2700
20% loss = Rs. 2700
The price at which she bought washing machine = Rs. 13,500 +Rs. 2700 = Rs. 16,200
7.) (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.
ANSWER:
Given that,
Chalk contains calcium, carbon and oxygen in the ratio 10:3:12
We have to find the percentage of carbon in chalk.
Total parts of Chalk = 10 + 3 +12 = 25
Now carbon parts are 3 out of 25.
3/25
We have to convert given fractional numbers to per cents.
We multiply and divide by 100
3/25x 100/100
We know, 1/100 = %
3/25x 100%
300% / 25
3/25 = 12%
Percentage of carbon in chalk is 12%
(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?
ANSWER:
Given that,
in a stick of chalk, carbon is 3g
We have to find weight of the chalk stick
We know,
12% is carbon.
12% = 3g
100% = ?
We do cross multiplication.
3 x 100% / 12%
= 25 gm.
Weight of the chalk stick is 25 gm.
8.) Amina buys a book for Rs. 275 and sells it at a loss of 15%. How much does she sell it for?
ANSWER:
Given that,
Amina buys a book for Rs. 275 and sells it at a loss of 15%.
We have to find how much she sells it for.
We 1st find 15% loss on Rs. 275
15% x Rs. 275
We know,
% = 1/100
15/100 x Rs. 275
= Rs. 41.25
14% loss = Rs. 41.25
She sells it for =Rs. 275 – Rs. 41.25
She sells it 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.
ANSWER:
Given, Principal = Rs. 1,200 at 12% p.a. and time = 3 years
We have to find the amount to be paid at the end of 3 years.
The amount to be paid at the end of 3 years =
We know,
Amount = Principal + Interest
Interest = P x R x T / 100
Interest = Rs. 1,200 x 12% x 3 / 100
Interest = Rs.432
The amount to be paid at the end of 3 years = Rs. 1,200 + Rs.432
The amount to be paid at the end of 3 years = Rs. 1,632
(b) Principal = Rs. 7,500 at 5% p.a.
ANSWER:
Given, Principal = Rs. 7,500 at 5% p.a.and time = 3 years
We have to find the amount to be paid at the end of 3 years.
The amount to be paid at the end of 3 years =
We know,
Amount = Principal + Interest
Interest = P x R x T / 100
Interest = Rs. 7,500 x 5% x 3 / 100
Interest = Rs.1125
The amount to be paid at the end of 3 years = Rs. 7,500 + Rs.1125
The amount to be paid at the end of 3 years = Rs. 8,625
10.) What rate gives Rs. 280 as interest on a sum of Rs. 56,000 in 2 years?
ANSWER:
Given,
Interest = Rs. 280
Principal = Rs. 56,000
Time = 2 year
We have to find rate of interest.
We know,
Interest = P x R x T / 100
Rs. 280 = Rs. 56,000 x R x 2 / 100
R = Rs. 280 x 100 / Rs. 56,000 x 2
R = 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:
Given,
Meena gives an interest of Rs. 45 for one year at 9% rate p.a.
We have to find what is sum she has borrowed. I.e. Principle.
We know,
Interest = P x R x T / 100
Rs. 45 = P x 9% x 1 / 100
P = Rs. 45 x 100 / 9
P = Rs.500
Sum she has borrowed is Rs.500