Comparing Quantities NCERT Exercise 8.2
Question 1: Convert the given fractional numbers to per cents.
(a) `1/8`
Answer: `1/8 xx 100 = 12.5%`
(b) `5/4`
Answer: `5/4 xx 100 = 125%`
(c) `(3)/(40)`
Answer: `(3)/(40) xx 100 = 7.5%`
(d) `2/7`
Answer: `2/7 xx 100 = 28.57%`
Question 2: Convert the given decimal fractions to per cents.
(a) 0.65
Answer: `0.65 xx 100 = 65%`
(b) 2.1
Answer: `2.1 × 100 = 210%`
(c) 0.02
Answer: `0.02 × 100 = 2%`
(d) 12.35
Answer: `12.35 xx 100 = 1235%`
Question 3: Estimate what part of the figures is coloured and hence find the per cent which is coloured.
Answer: (i) 25% (ii) 60% (ii) 37.5%
Question 4: Find:
(a) 15% of 250`
Answer: `(250 xx 15)/(100) = 37.5`
(b) 1% of 1 hour
Answer: Let us first convert 1 hour into seconds
1 hr `= 60 xx 60 = 3600` second
`3600 xx 1% = (3600 xx1)/(100) = 36` second
(c) 20% of Rs. 2500
Answer: `(2500 xx20)/(100) = Rs. 500`
(d) 75% of 1 kg
Answer: Let us first convert 1 kg into g
1 kg = 1000 g
`(1000 xx 75)/(100) = 750` g
Question 5: Find the whole quantity if
(a) 5% of it is 600.
Answer: Let us assume the whole quantity `= x`
`x\xx(5)/(100)=600`
Or, `x=(600xx100)/(5)=12000`
(b) 12% of it is Rs. 1080.
Answer: Let us assume the whole quantity `= x`
`x\xx(12)/(100)=1080`
Or, `x=(1080xx100)/(12)=9000`
(c) 40% of it is 500 km.
Answer: Let us assume the whole quantity `= x`
`x\xx(40)/(100)=500`
Or, `x=(500xx100)/(40)=1250` km
(d) 70% of it is 14 minutes.
Answer: Let us assume the whole quantity `= x`
`x\xx(70)/(100)=14`
Or, `x=(14xx100)/(70)=20` min
(e) 8% of it is 40 litres.
Answer: Let us assume the whole quantity `= x`
`x\xx(8)/(100)=40`
Or, `x=(40xx100)/(8)=500` liter
Question 6: Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
Answer:
`25%=(25)/(100)=1/4`
(b) 150%
Answer:
`150%=(150)/(100)=3/2=1\1/2`
(c) 20%
Answer:
`20%=(20)/(100)=1/5`
(d) 5%
Answer:
`5%=(5)/(100)=(1)/(20)`
Question 7: In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
Answer: Total = 100, females = 30%, males = 40% and children = ?
Or, 30% + 40% + children = 100%
Or, 70% + children = 100%
Or, children `= 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: Total = 100%, voted = 60% not voted = ?
Or, 60% + Did not vote = 100%
Or, Did not vote = 100% - 60% = 40%
Number of people who did not vote:
`=15000xx40%`
`=15000xx(40)/(100)=6000`
Question 9: Meeta saves Rs. 400 from her salary. If this is 10% of her salary. What is her salary?
Answer: Meeta’s salary can be calculated as follows:
`(400xx100)/(10)=Rs. 4000`
Alternate Method: When saving is Rs. 10 then salary is Rs. 100.
Hence, when saving is Rs. 1 then salary is 100/10
Hence, when saving is Rs. 400 then salary is
`(400xx100)/(10)=Rs. 4000`
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 matches won can be calculated as follows:
`20xx25%=20xx(25)/(100)=5`