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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