Question

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

Answer 1

Let three numbers let $a,b$ and $c$

$At.Q:a:b=2:3$ and $b:c=5:8$

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

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

$c=\frac{8b}{5}$

$\therefore$Sum of three numbers is $98$

$a+b+c=98$

$\frac{2b}{3}+b+\frac{8b}{5}=98$

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

$49b=1470$

$b=30$

$a=\frac{2\times 30}{3}c=\frac{8\times 30}{5}$

$a=20c=48$

$\therefore$ The numbers are

$20,30$ and $48$