Question

The difference between two whole numbers is $66$. The ratio of the two numbers is $5:2$. What are the two numbers?

Answer 1

We have,

Let the two whole number is x and y.

Then,

$x-y=66......\left(1\right)$

Now, Acoording to question,

$\frac{x}{y}=\frac{5}{2}$

$\Rightarrow 2x=5y$

$\Rightarrow x=\frac{5}{2}y$

Put in equation (1) and we get,

$x-y=66$

$\Rightarrow \frac{5}{2}y-y=66$

$\Rightarrow 5y-2y=66\times 2$

$\Rightarrow 3y=66\times 2$

$\Rightarrow y=\frac{66\times 2}{3}$

$\Rightarrow y=22\times 2$

$\Rightarrow y=44$

Put the value of y in equation (1) and we get,

$x-y=66$

$\Rightarrow x-44=66$

$\Rightarrow x=66+44$

$\Rightarrow x=110$

Then, the number is $110\text{and}44$

Hence, this is the answer.