Question

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

• A. $15$
• B. $20$
• C. $30$
• D. $32$

Answer 1

Answer: (C)

$30$

Suppose the number are $a,b,c$ then
$a+b+c=\mathrm{98...............}eq.\left(1\right)$
and $\frac{a}{b}=\frac{2}{3},\frac{b}{c}=\frac{5}{8}$

$\Rightarrow a=\frac{2b}{3},c=\frac{8b}{5}$

Substitute the value of $a$ and $b$ in $eq\left(1\right)$
$\frac{2b}{3}+b+\frac{8b}{5}=98$

$\Rightarrow \frac{10b+15b+24b}{15}=98$

$\Rightarrow 49b=98\times 15$

$\Rightarrow b=30$
Hence, option 'C' is correct.