Question

The ratio between the ages of Ajay and Vijay is 3:5 and the difference between their ages is 8 years, what will be the ratio of their ages after 8 years​

Answer 1

Answer:-

After seven years ratio of the ages of Ajay and Vijay would be 5:7.

Explanation:-

Given:-

• Ratio of present ages of Ajay and Vijay = 3:5.

To Find:-

• Ratio of their ages after 8 years.

Solution:-

Since ratio of ages of Ajay and Vijay is 3:5, this means:-

$\\ \tiny \textbf{ \mapsto Present Age of Ajay \ratio Present Age of Vijay = 3 \ratio 5.}$

$\\ \bf{\mapsto\:\:\dfrac{Age\:\: of\:\: Ajay}{Age \:\:of \:\:Vijay} = \dfrac{3}{5}.}$

Which means present age of Ajay must be multiple of 3 and present of age of Vijay must be multiple of 5.

So let the present age of Ajay be 'x' and present age of Vijay be 'y'.

So ATQ:-

$\\ \tt\mapsto 5x - 3x = 8.$

$\\ \tt\mapsto2x = 8.$

$\\ \tt\mapsto x = \dfrac{8}{2} .$

$\\ \large\tt\mapsto \boxed{ \bf x = 4}$

So we get the value of x which is 4.

Therefore,

Present age of Ajay,

$\\ \large \bf = 3x = 3 \times 4 = 12.$

Present age of Vijay,

$\\ \large \bf = 5x = 5 \times 4 = 20.$

And Hence present ages of Ajay and Vijay ate 12 and 20 respectively.

Now,

Age of Ajay after 8 years = 12 + 8 = 20.

Age of Vijay after 8 years = 20 + 8 = 28.

Therefore,

Ratio of their ages after 8 years,

$= \tt \cancel{20} \ratio \cancel{28}.$

$\boxed{ = \bf \large 5 \ratio7.}$

Therefore the ratio of their ages after 8 years would be 5:7.