The difference of the two number is 50 if the smaller number is divided by the greater number, the fraction obtained is $\frac{3}{8}$. Find the numbers.

Given: 

Difference between two numbers $= 50$.

When the smaller number is divided by the greater number, the fraction obtained is $\frac{3}{8}$.

To find: 

We have to find the numbers.

Solution:

Let the small number be $p$

Then,

Greater number $= p + 50$

Therefore,

$\frac{p}{p+50}=\frac{3}{8}$

$8(p) =3(p+50)$       (On cross multiplication)

$8p=3p+150$

$8p-3p=150$

$5p=150$

$p=\frac{150}{5}$

$p = 30$

So,

The small number $= p = 30$

The greater number $= p+50 = 30+50 = 80$

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Updated on: 10-Oct-2022

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