Class 7 Maths

# 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:

• Rs. 5 to 50 paise

Answer: Rs. 5 = 500 paise
Ratio = 500 ÷ 50 = 10 : 1
• 15 kg to 210 g

Answer: 15 kg = 15000 g
Ratio = 15000 ÷ 210 = 500 : 7
• 9 m to 27 cm

Answer: 9 m = 900 cm
Ratio = 900 ÷ 27 = 100 : 3
• 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 km2 and area of UP = 2 lakh km2.

• How many people are there per km2 in both these States?