Ratio and Proportion (अनुपात और समानुपात)
A ratio is a comparison of the sizes of two or more quantities of the same kind by division.
If a and b are two quantities of the same kind (in same units), then the fraction a/b is called the ratio of a to b. It is written as a : b. Thus, the ratio of a to b = a/b or a : b. The quantities a and b are called the terms of the ratio, a is called the first term or antecedent and b is called the second term or consequent.
For example, in the ratio 5 : 6, 5 & 6 are called terms of the ratio. 5 is called first term and 6 is called second term.
Questions:
Q.1 The ratio of first class and second class train fares between two stations is 5: 3 and number of passengers travelling by first and second class is 1:45. If Rs. 5628 is collected as fare, what is the amount that is collected from first class passengers?
(a) Rs. 137 (b) Rs. 105 (c) Rs. 201 (d) Rs. 210
Q.2 The ratio to Suhana's height to her father's height is 6:11. Suhana is 1.02 m tall. How tall is her father?
(a) 0.8 m (b) 0.56 m (c) 1.57 m (d) 1.87 m
Q.3 Which of the following ratio is the largest?
(a) 1:33 (b) 1:4 (c) 5:8 (d) 2:3
Q.4 In two types of stainless steel, the ratio between chromium and steel are 2:11 and 5:21 respectively. If these two types of stainless steel are mixed together to form a new stainless steel in which the ratio of chromium to steel is 7:32, then find the ratio in which these two types of stainless steel are to be mixed together.
(a) 3:4 (b) 1:2 (c) 2:3 (d) 2:1
Q.5 If Rs.896 be divided into three parts, proportional to 𝟏/𝟐 : 𝟐/𝟑 : 𝟏/𝟔 then last part is
(a) Rs.448 (b) Rs.112 (c) Rs.336 (d) Rs.432
Q.6 The ratio of areas of 2 squares is 4:5. If the area of the bigger square is 400 cm². What is the total area of both the square? 2
(a) 900 cm² (b) 720 cm² (c) 3600 cm² (d) 320 cm²
Q.7 What should be added to each of the numbers 39, 42, 9 and 10 to get the numbers which are in proportion?
(a) 2 (b) 7 (c) 9 (d) 6
Q.8 A sum of Rs.8772 is divided among Anuj, Chandan and Bikram in such a way that the shares of Anuj and Chandan are in the ratio 2:3 and those of Chandan and Bikram are in the ratio 5:6. Find Chandan's share
(a) Rs.4312 (b) Rs.2341 (c) Rs.2041 (d) Rs.3060
Q.9 Express the ratio in its simplest form: 48 secs : 1(1/3) hours
(a) 3:5 (b) 36:1 (c) 1: 100 (d) 4:3
Q.10 The sum of the square of three numbers which are in the ratio of 3:4:5 is 1250. Largest number is.
(a) 15 (b) 30 (c) 20 (d) 25
Complete Video Solution of these Question : Video Link
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Answer Key:
1 - C
2 - D
3 - D
4 - B
5 - C
6 - B
7 - D
8 - D
9 - C
10 - D