Question

The sum of three numbers is 147. If the ratio of first to second is 2:3 and that of the second to the third is 5:8 then the second number is
A) 30 B) 72 C) 45 D) 36

Answer 1

Answer:

Option C is the answer for the given problem

Answer 2

The second number is 45.

Given:-

Sum of three numbers is 147

Ratio between first and second is 2:3

Ratio between second and third is 5:8

To Find:- The second number

Solution:-

Let the three numbers be x, y and z

⇒ x + y + z = 147

⇒x : y =2:3

⇒y : z = 5: 8

First we need to find the actual ratios between these three numbers, such that

$\frac{x}{y}$=$\frac{2}{3}$ and $\frac{y}{z}$= $\frac{5}{8}$

To make the value of y equal in both the fraction we need to multiply $\frac{x}{y}$ with 5 and $\frac{y} {z}$ with 3, we get

$\frac{x}{y}$ = $\frac{10}{15}$ and $\frac{y}{z}$= $\frac{15}{24}$

So, the final ratio will be

x : y : z = 10:15:24

If we add these ratios, we get

10+15+24 = 49 which is equal to 147

49⇒147

1⇒3 ( dividing 147 by 49)

Hence, from the given ratio, The second number, b = 15×3

= 45

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