# Ratio and Proportion

1. Divide 81 rupees in 2 : 7 ratio.

A. 18, 63

B. 63, 18

C. 38, 61

D. 16, 38

Ans: A

Explanation:

$\text&space;{Sum&space;of&space;ratio&space;=&space;2&space;+&space;7&space;=&space;9}&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text{First&space;find&space;sum&space;of&space;ratio}&space;\right&space;]$

$\text&space;{First&space;share}&space;=&space;\frac{2}{9}\times&space;81&space;=&space;18$

$\text{Second&space;share&space;}&space;=&space;\frac{7}{9}\times&space;81&space;=&space;63$

2. The triplicate ratio of 1 : 3 is

A. 1 : 4

B. 1 : 8

C. 9 : 1

D. 1 : 9

Ans: D

Explanation:

$\text&space;{Triplicate&space;ratio&space;of&space;1}&space;:&space;3&space;=&space;1\times&space;1&space;\times&space;1&space;:&space;3&space;\times&space;3\times&space;3&space;=&space;1&space;:&space;9$

3. The duplicate ratio of 4 : 3 is

A. 16 : 9

B. 8 : 6

C. 9 : 16

D. 3 : 4

Ans: A

Explanation:

$\text&space;{duplicate&space;ratio&space;of&space;4}&space;:&space;3&space;=&space;4\times&space;4&space;:&space;3\times&space;3&space;=&space;16&space;:&space;9$

4. The inverse ratio of 3 : 2 is

A. 3 : 2

B. 2 : 3

C. 9 : 4

D. 4 : 9

Ans: B

Explanation:

$\text&space;{Inverse&space;ratio&space;of&space;3&space;:&space;2&space;is&space;2&space;:&space;3}&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text{Inverse&space;ratio&space;of&space;a&space;:&space;b&space;=&space;b&space;:&space;a}&space;\right&space;]$

5. Find the fourth proportional to the numbers 6, 8 and 9.

A. 6

B. 8

C. 9

D. 12

Ans: D

Explanation:

$\text&space;{Fourth&space;proportional}&space;=&space;\frac{b&space;\times&space;c}{a}$

$\text&space;{Let&space;x&space;be&space;the&space;fourth&space;proportional}$

$x&space;=&space;\frac{8&space;\times&space;9}{6}&space;=&space;12$

6. find the third proportional to 1 and 2.

A. 1

B. 2

C. 3

D. 4

Ans: D

Explanation:

$\text&space;{Third&space;proportional}&space;=&space;\frac{b^{2}}{a}$

$\text&space;{Let}&space;\,\,&space;x&space;\,\,&space;\text&space;{be&space;the&space;third&space;proportional}$

$x&space;=&space;\frac{2^{2}}{1}&space;=&space;\frac{2\times&space;2}{1}&space;=&space;4$

7. The mean proportional between 12 and 3 is

A. 12

B. 3

C. 6

D. 9

Ans: C

Explanation:

$\text&space;{Let}&space;\,\,&space;x&space;\,\,&space;\text&space;{be&space;the&space;mean&space;proportional}$

$x&space;=&space;\sqrt{12\times3}&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text&space;{mean&space;proportional}&space;=&space;\sqrt{ab}&space;\right&space;]$

$x&space;=&space;\sqrt{36}&space;=&space;6$

8. The ratio between two quantities is 5 : 8. If the first quantity is 65kgs  find the other.

A. 96

B. 98

C. 102

D. 104

Ans: D

Explanation:

$\text&space;{Let&space;the&space;other&space;quantity&space;be}&space;\,\,&space;x&space;\,\,&space;\text&space;{kgs.}$

$\text&space;{The&space;desired&space;ratio&space;is}&space;\,\,&space;65&space;:&space;x&space;\,\,&space;\text&space;{which&space;is&space;given&space;as&space;5&space;:&space;8}$

$5&space;:&space;8&space;=&space;65&space;:&space;x$

$5x&space;=&space;8&space;\times&space;65$

$x&space;=&space;\frac{8\times&space;65}{5}&space;=&space;104$

9. What number has 5 : 1 ratio to the number 10.

A. 42

B. 50

C. 55

D. 62

Ans: B

Explanation:

$\text&space;{Let}&space;\,\,x&space;\,\,&space;\text&space;{be&space;the&space;number}$

$\text&space;{Given}&space;\,\,&space;x&space;:&space;10&space;\,\,&space;\text&space;{in&space;the&space;ratio&space;of&space;5&space;:&space;1}$

$x&space;:&space;10&space;=&space;5&space;:&space;1$

$x&space;\times&space;1&space;=&space;5&space;\times&space;10&space;\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,&space;\left&space;[&space;\text&space;{product&space;of&space;means&space;=&space;product&space;of&space;extremes}&space;\right&space;]$

$x&space;=&space;50$

10. If A : B = 3 : 4 and B : C = 8 : 9, Then A : C is

A. 1 : 3

B. 3 : 2

C. 2 : 3

D. 1 : 2

Ans: C

Explanation:

$\frac{A}{B}&space;=&space;\frac{3}{4}&space;,&space;\frac{B}{C}&space;=&space;\frac{8}{9}$

$\frac{A}{C}&space;=&space;\left&space;(&space;\frac{A}{B}\times&space;\frac{B}{C}&space;\right&space;)&space;=&space;\left&space;(&space;\frac{3}{4}&space;\times&space;\frac{8}{9}&space;\right&space;)&space;=&space;\frac{2}{3}$

$A&space;:C&space;=&space;2&space;:&space;3$