Question

The sum of three numbers is 98. If the ratio of the first to second is 2:3 and that of the second to the third is 5:8, then the second number is

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Answer 1

Let the three parts be A, B, C. Then,

A : B = 2 : 3 and B : C = 5 : 8 = 5 $\times$ $\frac{3}{5}$:8 $\times$ $\frac{3}{5}$ = 3:$\frac{24}{5}$

$\to$ A:B:C = 2:3:$\frac{24}{5}$ = 10:15:24

$\to$ B = $\frac{15}{49}$ $\times$ 98 = 30