# Comparing Quantities

**Ratio:** For comparing two ratios, we need to convert them to like fractions. When the two fractions are equal, then the two given ratios are equal.

**Proportion:** If two ratios are equal then given four quantities are said to be in proportion.

**Converting fractions or decimals into percentage:** For this, multiply the given fraction or decimal by 100.

**Converting percentage into fractions or decimals:** For this, divide the given percentage by 100.

**Simple Interest:** When P is principal, r is the rate of interest per annum and t is the time in years, then simple interest is given by following formula:

`SI = (P xx r xx t) ÷ 100`

`P = (SI xx 100)/ (r xx t)`

`r = (SI xx 100)/(P xx t)`

`t = (SIxx 100)/(P xx r)`

Profit percentage `= (text(Profit)xx 100)/text(Cost Price)`

Loss percentage `= (text(Loss) xx 100)/ text(Cost Price)`

Cost Price `= (text(Selling Price) xx 100)/(100 + %text(Profit))`

Cost Price `= (text(Selling Price) xx 100)/(100 - %text(Loss))`

## Exercise 8.1

**Question 1:** Find the ratio of:

(a) Rs. 5 to 50 paise

**Answer:** Rs. 5 = 500 paise

Ratio `= 500 ÷ 50 = 10 : 1`

(b) 15 kg to 210 g

**Answer:** 15 kg = 15000 g

Ratio `= 15000 ÷ 210 = 500 : 7`

(c) 9 m to 27 cm

**Answer:** 9 m = 900 cm

Ratio `= 900 ÷ 27 = 100 : 3`

(d) 30 days to 36 hours

**Answer:** 30 days `= 30 xx 24 = 720` hours

Ratio `= 720 ÷36 = 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:** Since, every 6 students need 3 computers.

Hence, every 1 student needs 3 ÷6 computers.

Hence, every 24 students need `(3 ÷ 6) xx 34 = 12` computers

**Question 3:** Population of Rajasthan = 570 lakhs and population of UP = 1660 lakhs. Area of Rajasthan = 3 lakh km^{2} and area of UP = 2 lakh km^{2}.

(a) How many people are there per km^{2} in both these States?

**Answer:** Population ÷ Area

Rajasthan = 570 ÷ 3 = 190 people per square km

UP = 1660 ÷ 2 = 830 people per square km

(b) Which State is less populated?

**Answer:** Rajasthan