# Comparing Quantities

## Exercise 8.1

Question 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.

**Answer:** Required Ratio `=(15)/(30)=1/2=1∶2`

(b) 5 m to 10 km

**Answer:** Required Ratio `=(5)/(10)=1/2=1∶2`

(c) 50 paise to Rs 5

**Answer:** Rs 5 = 500 paise

Ratio `=(50)/(500)=(1)/(10)=1∶10`

Question 2: Convert the following ratios to percentages.

(a) 3 : 4

**Answer:** `3∶4=3/4`

On multiplying by 100 you get, `3/4xx100=75%`

(b) 2 : 3

**Answer:** `2∶3=2/3`

On multiplying by 100 you get, `2/3xx100=66(2)/(3)%`

Question 3: 72% of 25 students are good in mathematics. How many are not good in mathematics?

**Answer:** Percentage of Students not good in math `= 100 - 72 = 28`

Number of students not good in Math `=25xx(28)/(100)=7`

Or, you can calculate as follows also:

Number of students good in Math `=25xx(72)/(100)=18`

So, number of students not good in Math `=25-18=7`

Question 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?

**Answer:** Let us assume total number of matches `=x`

Then, `x\xx40%=10`

Or, `x=10xx(100)/(40)=25`

So, total number of matches played = 25

**Alternate Method:**

Since, when the team won 40 matches, number of total matches is 100

Hence, when team won 1 match, number of total matches `=(100)/(40)`

Hence, when team won 10 matches, number of total matches `=(100)/(40)xx10=25`

Question 5: If Chameli had Rs 600 left after spending 75% of her money, how much did she have in the beginning?

**Answer:** Money left after spending `75% = 100-75 = 25%`

Let us assume total money = x

Then, `x\xx25%=600`

Or, `x=600xx(100)/(25)=2400`

Chameli had Rs. 2,400 in the beginning

Question 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.

**Answer:** Cricket Fans = 60%

Football Fans = 30%

So, Other Sports’ Fans `= 100 - (60 + 30) = 10%` people like other games.

Number of cricket fans `=50,00,000xx(60)/(100)=30,00,000`

Number of football fans `=50,00,000xx(30)/(100)=15,00,000`

Number of other sports fans `=50,00,000xx(10)/(100)=5,00,000`