Question

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

• A. 27
• B. 33
• C. 49
• D. 55

Answer 1

The correct option is B

33

Let the number be $3x$ and $5x$. Then, $\frac{3x-9}{5x-9}=\frac{12}{23}$

$\Rightarrow 23(3x-9)=12(5x-9)$

$\Rightarrow 9x=99$

$\Rightarrow x=11$

$\therefore$ The smaller number = $(3\times 11)=33$.