Question

The sum of three numbers is $116.$ The ratio of the second to the third is $9:16$ and the first to third is $1:4.$ The second number is

• A. $30$
• B. $32$
• C. $34$
• D. $36$

Answer 1

The correct option is D $36$

Let the 1st number be $x$. Then, third number $=4x$
Given, $\frac{\text{2nd number}}{\text{3rd number}}=\frac{9}{16}\Rightarrow \frac{\text{2nd number}}{4x}=\frac{9}{16}$
$\Rightarrow \text{2nd number}=\frac{9}{16}\times 4x=\frac{9}{4}x$
Given, $x+\frac{9x}{4}+4x=116$
$\Rightarrow 4x+9x+16x=116\times 4$
$\Rightarrow 29x=116\times 4\Rightarrow x=\frac{116\times 4}{29}=16$
$\therefore \text{2nd number}=\frac{9}{16}\times 4\times 16=36$