Question

Find two numbers in the ratio of 7 : 12 so that the greater exceeds the less by 275.

Answer 1

Let the two numbers be $a:b$ and assume that $b>a$

Given that $\frac{a}{b}=\frac{7}{12}$ and $b-a=275$

$\Rightarrow b=a+275$

Substitute above equation in $\frac{a}{b}=\frac{7}{12}$

$\Rightarrow \frac{a}{a+275}=\frac{7}{12}$

$\Rightarrow 12a=7a+7\times 275$

$\Rightarrow a=7\times 55=385$

So the value of $b=a+275=385+275=660$

Therefore the two numbers are $385,660$