Question

Two numbers are in the ratio $1\frac{1}{2}:2\frac{2}{3}$. When each of these is increased by $15$, they become in the ratio $1\frac{2}{3}:2\frac{1}{2}$. Find the greater number.

• A. $27$
• B. $36$
• C. $48$
• D. $64$

Answer 1

The correct option is C $48$

Let the numbers be $\frac{3}{2}x$ and $\frac{8}{3}x$.

Then, $\frac{\frac{3x}{2}+15}{\frac{8x}{3}+15}=\frac{\frac{5}{3}}{\frac{5}{2}}\Rightarrow \frac{\frac{3x+30}{2}}{\frac{8x+45}{3}}=\frac{2}{3}$

$\Rightarrow \frac{3x+30}{8x+45}\times \frac{3}{2}=\frac{2}{3}$

$\Rightarrow \frac{3x+30}{8x+45}=\frac{4}{9}$

$\Rightarrow 27x+270=32x+180$

$\Rightarrow 5x=90\Rightarrow x=18$.

$\therefore Thegreaternumber=\frac{8}{3}\times 18=48$.