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Comparing Quantities : Exercise 8.1 (Mathematics NCERT Class 8th)


Q.1 Find the ratio of the following.
(a) Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.
(b) 5 m to 10 km (c) 50 paise to Rs 5
Sol. (a) The ratio of speed of a cycle to the speed of scooter = {{15} \over {30}} = {1 \over 2} = 1:2

(b) We know that, 1 km = 1000 m. So, 10 km = 10 x 1000 = 10,000 m
Therefore, required ratio = {{5m} \over {10km}} = {{5m} \over {10,000m}} = {1 \over {2000}} = 1:2000

(c) We know that, 1 Rs = 100 paise. So, 5 Rs = 500 paise
Therefore, required ratio = {{50paise} \over {5Rs}} = {{50paise} \over {500paise}} = {1 \over {10}} = 1:10

Q.2 Convert the following ratios to percentages.
(a) 3 : 4 (b) 2 : 3
Sol. (a) 3:4
Percentage of 3 : 4 = {3 \over 4} \times 100\% = 75\%

(b) 2 : 3
Percentage of 2 : 3 = {2 \over 3} \times 100\% = 66{2 \over 3}\%

Q.3 72% of 25 students are good in mathematics. How many are not good in mathematics?
Sol. Given, 72% of 25 students are good in mathematics.
Therefore, percentage of students not good in mathematics = (100 – 72)% = 28%
Hence, number of students not good in mathematics = {{28} \over {100}} \times 25 = 7
Thus, there are 7 students not good in mathematics.

Q.4 A football team won 10 matches out of the total number of matches they played. If their win percentage was 40, then how many matches did they play in all?
Sol. Let the total number of matches played be x.
Given, team had won 10 matches and the winning percentage of the team was 40%.
Therefore, {{40} \over {100}} \times x = 10
x = 10 \times {{40} \over {100}}
x = 25
Hence, the team had played 25 matches.

Q.5 If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?
Sol. Let the amount Chamlei had in the beginning be x.
Given, Chameli had Rs 600 left after spending 75% of her money.
Therefore, (100 - 75)\% of x = Rs 600
25%of x = Rs 600
{{25} \over {100}} \times x = 600Rs
x = 600 \times {{100} \over {25}} Rs
x = 2400Rs
Hence, Chameli had Rs 2400 in the beginning.

Q.6 If 60% people in a city like cricket, 30% like football and the remaining like other games, then what per cent of the people like other games? If the total number of people are 50 lakh, find the exact number who like each type of game.
Sol. Given, Number of people who like cricket = 60% and number of people who like football = 30%.
Therefore, number of people who like other games = 100% - (60% + 30%) = 10%
Given, total number of people = 50 lakh
Hence, number of people who like cricket = \left( {{{60} \over {100}} \times 50} \right) = 30lakh
Number of people who like cricket = \left( {{{30} \over {100}} \times 50} \right) = 15lakh
Number of people who like cricket = \left( {{{10} \over {100}} \times 50} \right) = 5lakh
Thus, number of people who like other games are 5 lakh.



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