Question

Two numbers are in the ratio $3:5$. If $9$ is subtracted from each, the new numbers are in the ratio $12:23$. Find the smaller number.

• A. $27$
• B. $33$
• C. $49$
• D. $55$

Answer 1

Answer: (B)

$33$

Let the numbers be $x$ and $y$

$\frac{x}{y}=\frac{3}{5}$ ...(1)

According to the question,

$\frac{x-9}{y-9}=\frac{12}{23}$ ...(2)

$x=\frac{3y}{5}$

$\frac{\frac{3y}{5}-9}{y-9}=\frac{12}{23}$

$\frac{3y-45}{5y-45}=\frac{12}{23}$

$23(3y-45)=12(5y-45)$

$69y-1035=60y-540$

$9y=1035-540=495$

$y=55$

From (1)

$\frac{x}{55}=\frac{3}{5}$

Thus the smaller number is 33