Question

Three numbers are in the ratio $\frac{1}{2}:\frac{2}{3}:\frac{3}{4}$. The difference between the greatest and the smallest numbers is $36$. The numbers are

• A. $72,84,108$
• B. $60,72,96$
• C. $72,84,96$
• D. $72,96,108$

Answer 1

The correct option is D $72,96,108$

The three numbers are in the ratio $\frac{1}{2}:\frac{2}{3}:\frac{3}{4}$,
$i.e.,\frac{1}{2}\times 12:\frac{2}{3}\times 12:\frac{3}{4}\times 12,i.e.,6:8:9$.
Let the number be $6x,8x$ and $9x$.
Given, $9x-6x=36$
$\Rightarrow 3x=36\Rightarrow x=12$
$\therefore$The numbers are $72,96$ and $108$.