Question

Two numbers are in the ratio of 4 : 5. If 30is subtracted from each of the numbers , the ratio becomes 1 : 2. Find the numbers.

Answer 1

Given :

• Two numbers are in the ratio of 4 : 5.
• If 30 is subtracted from each of the numbers , the ratio becomes 1 : 2.

To Find :

• The numbers .

Solution :

$\longmapsto\tt{Let\:First\:No.\:be=4x}$

$\longmapsto\tt{Let\:Second\:No.\:be=5x}$

Now ,

• If 30 is subtracted from each of the numbers , the ratio becomes 1 : 2.

$\longmapsto\tt{First\:Number=4x-30}$

$\longmapsto\tt{Second\:Number=5x-30}$

A.T.Q :

$\longmapsto\tt{\dfrac{4x-30}{5x-30}=\dfrac{1}{3}}$

$\longmapsto\tt{2(4x-30)=1(5x-30)}$

$\longmapsto\tt{8x-60=5x-30}$

$\longmapsto\tt{8x-5x=-30+60}$

$\longmapsto\tt{3x=30}$

$\longmapsto\tt{x=\cancel\dfrac{30}{3}}$

$\longmapsto\tt\bf{x=10}$

Value of x is 10 ...

Therefore :

$\longmapsto\tt{First\:Number=4(10)}$

$\longmapsto\tt\bf{40}$

$\longmapsto\tt{Second\:Number=5(10)}$

$\longmapsto\tt\bf{50}$