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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Updated on: 10-Oct-2022

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