Question

The sum of 3 numbers is 136. If the ratios between first and second be 2 : 3 and that between second and third is 5 : 3, then the second number is 
1. 48
2. 60
3. 40
4. 52

Answer 1

Correct Answer - Option 2 : 60

Given:

Sum of 3 numbers = 136

First number : Second number = 2 : 3

Second number : Third number = 5 : 3

Concept used:

If the ratio of A : B and B : C is given 

Then, to find ratio of A : B : C

To make ratio of B equal we have to apply the formula below.

A : B₁ and B₂ : C

A : B : C = A × B₂ : B₁ × B₂ : B₂ × C

Calculation:

Let the first, second and third numbers be A,B and C respectively.

⇒ A + B + C = 136

A : B = 2 : 3

B : C = 5 : 3

⇒ A : B : C = 10 : 15 : 9

⇒ A + B + C = 10x + 15x + 9x

⇒ A + B + C = 34x

⇒ 34x = 136

⇒ x = 4

⇒ B = 15x 

⇒ B = 60

∴ The second number is 60.