Question

Two numbers are in the ratio $1\frac{1}{2}:2\frac{2}{3}$. But if each number is increased by $15$. then the ratio becomes $1\frac{2}{3}:2\frac{1}{2}$. The numbers are:

• A. $27,42$
• B. $36,48$
• C. $27,48$
• D. $27,36$

Answer 1

The correct option is C $27,48$

The ratio of two numbers $1\frac{1}{2}:2\frac{2}{3}=\frac{3}{2}:\frac{8}{3}$ $=9:16$

Let the two numbers are $9x$ and $16x$.

According to the given condition,

$\Rightarrow$ $\frac{9x+15}{16x+15}=1\frac{2}{3}:2\frac{1}{2}=\frac{5}{3}:\frac{5}{2}$

$\Rightarrow$ $\frac{9x+15}{16x+15}=\frac{2}{3}$

$\Rightarrow$ $3\times (9x+15)=2\times (16x+15)$

$\Rightarrow$ $27x+45=32x+30$

$\Rightarrow$ $5x=15$

$\therefore$ $x=3$

$\therefore$ The numbers are $9x=9\times 3=27$ and $16x=16\times 3=48$.