Question

Two numbers are in the ratio 4:5. If 10 is added to both the numbers, ratio becomes 2:1. Find the numbers.

• A. $\frac{-20}{3}$ and $\frac{-25}{3}$
• B. $\frac{-21}{3}$ and $\frac{-25}{3}$
• C. $\frac{-22}{3}$ and $\frac{-25}{3}$
• D. $\frac{-23}{3}$ and $\frac{-25}{3}$

Answer 1

The correct option is A $\frac{-20}{3}$ and $\frac{-25}{3}$

Let us assume numbers are $4x$ and $5x$.
When 10 is added to both the numbers,
The number becomes $(4x+10)$ and $(5x+10)$

Since the new ratio is $2:1$
$\frac{(4x+10)}{(5x+10)}=\frac{2}{1}$

By cross multiplying,
$4x+10=2(5x+10)$
$4x+10=10x+20$
$10x-4x=10-20$
$6x=-10$
$x=\frac{-5}{3}$

Therefore numbers are,
$4x=4\times \left(\frac{-5}{3}\right)=\frac{-20}{3}$

$5x=5\times \left(\frac{-5}{3}\right)=\frac{-25}{3}$