Question

The sum of the three number is $68$. If the ratio of the first to second is $3:2$ and that of the second to the third is $5:3$, then the second number is

Answer 1

Sum of three numbers$=68$

Let $x,y,z$ be the three numbers.

Given$:x+y+z=68$

$x:y=3:2\Rightarrow \frac{x}{y}=\frac{3}{2}$

$y:z=5:3\Rightarrow \frac{y}{z}=\frac{5}{3}$

$\Rightarrow 2x=3y\Rightarrow y=\frac{2x}{3}$ and $3y=5z\Rightarrow z=\frac{3y}{5}=\frac{3\times \frac{2x}{3}}{5}=\frac{2x}{5}$

From above $x+y+z=68$

$\Rightarrow x+\frac{2x}{3}+\frac{2x}{5}=68$

$\Rightarrow \frac{15x}{15}+\frac{10x}{15}+\frac{6x}{15}=68$

$\Rightarrow \frac{15x+10x+6x}{15}=68$

$\Rightarrow 31x=68\times 15$

$\therefore x=\frac{68\times 15}{31}=\frac{1020}{31}$

$\therefore$ the second number $y=\frac{2x}{3}=\frac{2\times \frac{1020}{31}}{3}=\frac{680}{31}$