Question

# The sum of three numbers is $$98$$. The ratio of the first to the second term is $$\displaystyle\frac{2}{3}$$ and the ratio of the second to the third is $$\displaystyle\frac{5}{8}$$. Then the second number is

A
15
B
20
C
30
D
32

Solution

## The correct option is B $$30$$Suppose the number are $$a,b,c$$ then$$a+b+c= 98...............eq.\left ( 1 \right )$$and $$\dfrac{a}{b}=\dfrac{2}{3},\dfrac{b}{c}=\dfrac{5}{8}$$$$\Rightarrow a=\dfrac{2b}{3},c=\dfrac{8b}{5}$$ Substitute   the   value   of   $$a$$   and   $$b$$   in  $$eq\left ( 1 \right )$$$$\dfrac{2b}{3}+b+\dfrac{8b}{5}=98$$$$\Rightarrow \dfrac{10b+15b+24b}{15}=98$$$$\Rightarrow 49b=98\times15$$$$\Rightarrow b=30$$    Hence, option 'C' is correct.Mathematics

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