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1. Find the ratio of the following:
(a) Speed of a cycle 15 km per hour to the speed of a scooter 30 km per hour.
(b) 5 m to 10 km
(c) 50 paise to ₹ 5
Solution:
a) Ratio of the speed of the cycle to the speed of the scooter = \({15\over 30} = {1\over 2} = 1:2\)
b) Since 1 km = 1000 m
\({5 \text{m}\over 10 \text{km}} = {5 \text{m}\over (10 \times 1000)\text{m}} = {5\over 10000} = {1\over 2000} = 1:2000\)
(a) Speed of a cycle 15 km per hour to the speed of a scooter 30 km per hour.
(b) 5 m to 10 km
(c) 50 paise to ₹ 5
Solution:
a) Ratio of the speed of the cycle to the speed of the scooter = \({15\over 30} = {1\over 2} = 1:2\)
b) Since 1 km = 1000 m
\({5 \text{m}\over 10 \text{km}} = {5 \text{m}\over (10 \times 1000)\text{m}} = {5\over 10000} = {1\over 2000} = 1:2000\)
The required ratio is 1:2000
c) Since, ₹1 = 100 paise
\({50 \text{paise}\over 5} = {50\over (5 \times 100)} = {50\over 500} = {1\over10} = 1:10\)
The required ratio is 1:10
2. Convert the following ratio to percentages:
a) 3:4
b) 2:3
Solution:
a) \(3:4 = {3\over 4} = {3\over 4} \times 100\% = 0.75 \times 100\% = 75\%\)
b) \(2:3 = {2\over 3} = {2\over 3} \times 100\% = 0.666 \times 100\% = 66.66\% = 66{2\over 3}\%\)
3. 72% of 25 students are good in mathematics. How many are not good in mathematics?
Solution:
It’s given that 72% of 25 students are good in mathematics
So, the percentage of students who are not good in mathematics \(= (100 – 72)\% = 28\%\)
Here, the number of students who are good in mathematics \(= {72\over 100} \times 25 = 18\)
Thus, the number of students who are not good in mathematics = 25 – 18 = 7
[Also, 28% of 25 = \({28\over100} \times 25 = 7\)]
Therefore, 7 students are not good in mathematics.
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?
Solution:
Let the total number of matches played by the team be \(x\).
Given that the team won 10 matches and the winning percentage of the team was 40%.
\( {40\over100} \times x = 10\)
40x = 10 × 100
40x = 1000
\(x = {1000\over 40}\)
= 25
Therefore, the team played 25 matches.
5. If Chameli had ₹600 left after spending 75% of her money, how much did she have in the beginning?
Solution:
Let the amount of money which Chameli had, in the beginning, be \(x\)
Given that, after spending 75% of ₹\(x\), she was left with ₹600
So, (100 – 75)% of x = ₹600
Or, 25% of x = ₹600
\({25\over100} \times x =\) ₹600
Therefore, 7 students are not good in mathematics.
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?
Solution:
Let the total number of matches played by the team be \(x\).
Given that the team won 10 matches and the winning percentage of the team was 40%.
\( {40\over100} \times x = 10\)
40x = 10 × 100
40x = 1000
\(x = {1000\over 40}\)
= 25
Therefore, the team played 25 matches.
5. If Chameli had ₹600 left after spending 75% of her money, how much did she have in the beginning?
Solution:
Let the amount of money which Chameli had, in the beginning, be \(x\)
Given that, after spending 75% of ₹\(x\), she was left with ₹600
So, (100 – 75)% of x = ₹600
Or, 25% of x = ₹600
\({25\over100} \times x =\) ₹600
x = ₹600 × 4
= ₹2400
Therefore, Chameli had ₹2400 in the beginning.
6. If 60% of people in the 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 is 50 lakhs, find the exact number who like each type of game.
Solution:
Percentage of people who like other games = (100 – 60 – 30)%
= (100 – 90)%
= 10%
Total number of people = 50 lakhs
Number of people who like cricket \(= {60\over100} \times 50 = 30\) lakhs
Number of people who like football \(= {30\over100} \times 50 = 15\) lakhs
Number of people who like other games \(= {10\over100} \times 50 = 5\) lakhs
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