Question

The respective ratio between two positive numbers (X and Y) is 3:5. When 2 is added to both the numbers, the ratio between X and Y becomes 5:8. What is the difference between both the numbers?

• A. 2
• B. 12
• C. 9
• D. 6
• E. 3

Answer 1

The correct option is B 12

Let the two positive numbers be x and y.
Then, $\frac{x}{y}=\frac{3}{5}\left(given\right)$

$\Rightarrow x=\frac{3y}{5}\left(i\right)$
$and\frac{x+2}{y+2}=\frac{5}{8}\left(given\right)$
$\Rightarrow 8(x+2)=5(y+2)\Rightarrow 8x+16=5y+10$
$\Rightarrow 8x-5y=10-16$
$\Rightarrow 8\left(\frac{3y}{5}\right)-5y=-6[Putx=\frac{3y}{5}]$
$\Rightarrow 24y-25y=-30$
$\Rightarrow -y=-30\Rightarrow y=30andx=\frac{3y}{5}=\frac{3\times 30}{5}=18$
Difference between both the numbers $=30-18=12$