Question

Two number are such that the ratio between them is $4:7$. If each is increased by $4$, the ratio becomes $3:5$. The larger number is :

• A. $36$
• B. $48$
• C. $56$
• D. $64$

Answer 1

The correct option is C $56$

Let the numbers be $x$ and $y$, respectively.

$\frac{x}{y}=\frac{4}{7}$

$7x=4y$ $...........\left(1\right)$

If each number is increased by $4$, then

$\frac{x+4}{y+4}=\frac{3}{5}$

$5x+20=3y+12$

$5x-3y+8=0$ $...........\left(2\right)$

On solving equation $\left(1\right)$ and $\left(2\right)$, we get

$x=32,y=56$

Hence, the largest number is $56$.