Sum of three numbers is 98 . If ratio between first and second be 2: 3 and between second and third

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

A

$30$

B

$20$

C

$58$

D

$48$

Solution

Let, the numbers be $x, y$ and $z$. Then,

$x+y+z=98, \frac{x}{y}=\frac{2}{3}$ and $\frac{y}{z}=\frac{5}{8}$

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

So, $\frac{2 y}{3}+y+\frac{8 y}{5}=98$

$\frac{49 y}{15}=98$ or, $y=30$

Standard 13

Quantitative Aptitude

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