The difference between two natural number is 28, if the smaller number is $\frac{3}{4}$ of the greater number then find the numbers.
Given:
Difference between two numbers = 28
Smaller number is $\frac{3}{4}$ of the greater number.
To find: Here we have to find the value of the two numbers.
Solution:
Let the small number be = p
Then,
Greater natural number be = p $+$ 28
Also, given that the smaller number is $\frac{3}{4}$ of the greater number:
$p\ =\ \frac{3}{4} (p\ +\ 28)$
$\frac{4}{3} p\ =\ p\ +\ 28$
$\frac{4}{3} p\ -\ p\ =\ 28$
$\frac{4p\ -\ 3p}{3} \ =\ 28$
$\frac{p}{3} \ =\ 28$
$p\ =\ 28\ \times \ 3$
p = 84
So,
The small number be = p = 84
The greater number be = p $+$ 28 = 84 $+$ 28 = 112
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