Question

A positive number is $7$ times another number . If $15$ is added to both the numbers , then one of the new numbers becomes $\frac{5}{2}$ times the other new number. What are the numbers ?

Answer 1

Let the number be $x$

Then the other number $=\frac{x}{7}$

According to the condition ,

$x+15=\frac{5}{2}(\frac{x}{7}+15)$

$2(x+15)=\frac{5x}{7}+5\times 15$

$2x+30=\frac{5x}{7}+75$

On simplification we get,

$2x-\frac{5}{7}x=75-30$

$\frac{14-5}{7}x=45$

$\frac{9x}{7}=45$

$x=45\times \frac{7}{9}$

We get ,

$x=35$

Hence ,

One number $=35$

Other number $=\frac{35}{7}=5$

Therefore , the numbers are $35$ and $5$