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

 

\text {First share} = \frac{2}{9}\times 81 = 18

 

\text{Second share } = \frac{7}{9}\times 81 = 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 {Triplicate ratio of 1} : 3 = 1\times 1 \times 1 : 3 \times 3\times 3 = 1 : 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 {duplicate ratio of 4} : 3 = 4\times 4 : 3\times 3 = 16 : 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 {Inverse ratio of 3 : 2 is 2 : 3} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, \left [ \text{Inverse ratio of a : b = b : a} \right ]

 

 

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

A. 6

B. 8

C. 9

D. 12

Ans: D

Explanation:

\text {Fourth proportional} = \frac{b \times c}{a}

 

\text {Let x be the fourth proportional}

 

x = \frac{8 \times 9}{6} = 12

 

 

6. find the third proportional to 1 and 2.

A. 1

B. 2

C. 3

D. 4

Ans: D

Explanation:

\text {Third proportional} = \frac{b^{2}}{a}

 

 

\text {Let} \,\, x \,\, \text {be the third proportional}

 

x = \frac{2^{2}}{1} = \frac{2\times 2}{1} = 4

 

 

 

7. The mean proportional between 12 and 3 is

A. 12

B. 3

C. 6

D. 9

Ans: C

Explanation:

\text {Let} \,\, x \,\, \text {be the mean proportional}

 

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

 

x = \sqrt{36} = 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 {Let the other quantity be} \,\, x \,\, \text {kgs.}

 

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

 

5 : 8 = 65 : x

 

5x = 8 \times 65

 

x = \frac{8\times 65}{5} = 104

 

 

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

A. 42

B. 50

C. 55

D. 62

Ans: B

Explanation:

\text {Let} \,\,x \,\, \text {be the number}

 

\text {Given} \,\, x : 10 \,\, \text {in the ratio of 5 : 1}

 

x : 10 = 5 : 1

 

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

 

x = 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} = \frac{3}{4} , \frac{B}{C} = \frac{8}{9}

 

 

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

 

 

A :C = 2 : 3