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 km2 and area of UP = 2 lakh km2.
(a) How many people are there per km2 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