Question

Two numbers are in the ratio $2:3$. If eight is added to both the numbers, the ratio becomes $3:4$, then find the numbers.

Answer 1

Two numbers are in the ratio of $2:3$

So, $\frac{x}{y}=\frac{2}{3}$

Cross multiply to get: $3x=2y$

Or, $3x-2y=0$ …..(1)

If 8 is added in both numbers the ratio becomes $3:4$

So, $\frac{(x+8)}{(y+8)}=\frac{3}{4}$

Cross multiply to get: $4(x+8)=3(y+8)$

Or, $4x+32=3y+24$

Or, $4x-3y=-8$ …….(2)

Multiplying Eq1 by 4 and Eq 2 by 3 we have:

$12x-8y=0$ ………(3)

$12x-9y=-24$ …………(4)

Solving Eq3 and Eq4 we have $y=24$ and $x=16$