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1. 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:

A. 20

B. 30

C. 48

D. 58

Solution:

Let the three parts be A, B, C. Then,
A : B = 2 : 3 and B : C = 5 : 8

\begin{aligned} = (5 \times \frac{3}{5}) : (8 \times \frac{3}{5}) = 3 : \frac{24}{5} \\ \Rightarrow A : B : C = 2 : 3 : \frac{24}{5} = 10 : 15 : 24 \\ \Rightarrow B = 98 \times \frac{15}{49} = 30 \end{aligned}

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