Question

Two numbers are in the ratio $7:4$. If their difference is $72$, find the numbers.

Answer 1

Let the two numbers be $x$ and $y$

Given that the numbers are in the ratio is $7:4$

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

$⟹4x-7y=0$ ......(1)

Given that difference between the numbers is $72$

Therefore, $x-y=72$ .......(2)

$4\times \left(2\right)-\left(1\right)⟹3y=72$

$⟹y=24$

substituting $y=24$ in (2)

$⟹x-24=72$

$⟹x=96$

Therefore, the numbers are $96,24$