Exercise 8.1
Question 1: Find the ratio of:
(a) Rs5 to 50 paise
(b) 15 kg to 210 g
(c) 9 m to 27 cm
(d) 30 days to 36 hours
Answer 1: To find ratios, both quantities should be in same unit.
(a) Rs 5 to 50 paise
â‡’ 5 x 100 paise to 50 paise [âˆ´ Rs 1 = 100 paise]
â‡’ 500 paise to 50 paise
Thus, the ratio is = 500/50 = 10/1 = 10 : 1
(b) 15 kg to 210 g
â‡’ 15 x 1000 g to 210 g [âˆµ 1kg = 1000 g]
â‡’ 15000 g to 210 g
Thus, the ratio is = 15000/210 = 500/7 = 500:7
(c) 9 m to 27 cm
â‡’ 9 x 100 cm to 27 cm [âˆµ 1m = 100 cm]
â‡’ 900 cm to 27 cm
Thus, the ratio is = 900/27 = 100/3 = 100:3
(d) 30 days to 36 hours
â‡’ 30 x 24 hours to 36 hours [âˆµ 1 day = 24 hours]
â‡’ 720 hours to 36 hours
Thus, the ratio is = 720/36 = 20/1 = 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?
Answer 2:
âˆµ 6 students need = 3 computers
âˆµ 1 student needs = 3/6 computers
âˆµ 24 students need =
Thus, 12 computers will be needed for 24 students.
Question 3: Population of Rajasthan = 570 lakhs and population of U.P. = 1660 lakhs. Area of Rajasthan = 3 lakh km^{2} and area of U.P. = 2 lakh km^{2}.
(i) How many people are there per km^{2} in both states?
(ii) Which state is less populated?
Answer 3:
(ii) Rajasthan is less populated.
Exercise 8.2
Question 1: Convert the given fractional numbers to percent:
(a) 1/8
(b) 5/4
(c) 3/40
(d) 2/7
Answer 1:
Question 2: Convert the given decimal fractions to per cents:
(a) 0.65
(b) 2.1
(c) 0.02
(d) 12.35
Answer 2:
Question 3: Estimate what part of the figures is coloured and hence find the percent which is coloured.
Answer 3: (i) Coloured part = 1/4
âˆ´ Percent of coloured part =
(ii) Coloured part = 3/5
âˆ´ Percent of coloured part
(iii) Coloured part = 3/8
âˆ´ Percent of coloured part
= 37.5%
Question 4: Find:
(a) 15% of 250
(b) 1% of 1 hour
(c) 20% of 2500
(d) 75% of 1 kg
Answer 4: (a) 15% of 250
(b) 1% of 1 hours = 1% of 60 minutes = 1% of (60 x 60] seconds
(c) 20% of Rs 500
(d) 75% of 1 kg = 75% of 1000 g
Question 5: Find the whole quantity if:
(a) 5% of it is 600
(b) 12% of it is â‚¹1080
(c) 40% of it is 500 km
(d) 70% of it is 14 minutes
(e) 8% of it is 40 litres
Answer 5: Let the whole quantity be x in given questions:
Question 6: Convert given per cents to decimal fractions and also to fractions in simplest forms:
(a) 25%
(b) 150%
(c) 20%
(d) 5%
Answer 6:
S. No. | Per cents | 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 |
Question 7: In a city, 30% are females, 40% are males and remaining are children. What percent are children?
Answer 7: 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.
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 8: 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
Hence, 6,000 candidates did not vote.
Question 9: Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?
Answer 9: Let Meera's salary be Rs x.
Now, 10% of salary = Rs 400
â‡’ 10% of x = Rs 400
Hence, Meera's salary is Rs 4,000.
Question 10: A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?
Answer 10: Number of matches played by cricket team = 20
Percentage of won matches = 25%
Total matches won by them = 25% of 20
Hence, they won 5 matches.