 # Ratio and Proportion

## Ratio is the comparison of two or more quantities of the same kind by division. To compare two ratios, convert them into equivalent like fractions. If two ratios are equal, we say that they are in proportion and use the symbol ‘::’ or ‘=’. or we can say that, four numbers a, b, c and d are said to be in proportion, if the ratio of the first two terms is equal to the ratio of the last two terms, i.e., a : b :: c : d. If a : b = c : d, then a and d are called extremes; and b and c are called means. The terms a, b, c and d are said to be in proportion if the product of extremes is equal to the product of means. This is called cross product rule. Three quantities a, b and c are said to be in Continued Proportion if b2 = a.c. If a, b and c are in continued proportion, then b is called the mean proportional between a and c, a is called first proportional and c is called the third proportional. The first and the fourth term of a proportion are called extremes. If a, b and c are in continued proportion, then ‘a’ is called the first proportional. If a, b and c are in continued proportion, then ‘c’ is called the third proportional. Keywords: Antecedent and consequent

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• Q1

If 10 bananas costs Rs 20, find the cost of 7 bananas.

Marks:2

Cost of 10 bananas = Rs 20 Cost of 1 banana = Rs 20/10 = Rs 2 Cost of 7 bananas = Rs 7 2 = Rs 14

• Q2

If we divide Rs 20 between Jatin and Arnav in the ratio 3 : 2, how much will each of them get?

Marks:2

Sum of the two terms of the ratio (3 : 2) = 3 + 2
= 5
Jatin's share = (3/5) 20
= Rs 12
Arnav's share = (2/5) 20
= Rs 8

• Q3

In a school of 1800 students, 600 are girls. Find the ratio of boys to the total number of students.

Marks:2

Total no. of students in the school = 1800
Total no. of girls = 600
Total no. of boys = 1800 – 600 = 1200 Required ratio = 1200 : 1800 = 2 : 3

• Q4

The length, breadth and height of a building is 200 m, 175 m and 150 m respectively. Find the ratio of
(ii) length: height

Marks:2

Length of the building = 200 m

Breadth of the building = 175 m

Height of the building = 150 m 