Question

Two numbers are in the ratio of $1:2$. If $7$ be added to both, their ratio changes to $3:5$. The greater number is.

• A. $20$
• B. $24$
• C. $28$
• D. $32$

Answer 1

The correct option is C $28$

Let the numbers are $x$ and $y$ whose ratio is $1:2$

$\frac{x}{y}=\frac{1}{2}$

$\Rightarrow 2x=y$.......................................(1)

Given that when 7 added to both numbers, ratio changes to $3:5$

$\frac{x+7}{y+7}=\frac{3}{5}$

$\Rightarrow 5(x+7)=3(y+7)$

$\Rightarrow 5x+35=3y+21$

$\Rightarrow 5x-3y=21-35$

$\Rightarrow 5x-3y=-14$.................(2)

Put the value of $y=2x$ as per (1) we get

$5x-3\left(2x\right)=-14$

$5x-6x=-14$

$x=14$

Put the value of $x=14$ in (1) we get

$2\times 14=y$

$\Rightarrow y=28$

Then numbers are$14,28$

Then greater number is $28$.