Question

father age is three times more than his son after 4 years father and son age ratio will be 13:5 respectively what is the present age of father​

Answer 1

Given -

Age of father = 3 times age of son.

After 4 years their ratio =

Father: son = 13 : 5

Let's assume that

Present age of son = x.

Present age of father = 3x.

Ratio after 4 years.

We will add 4 in age of son and age of father.

$\frac{3x + 4}{x + 4}$

Given ratio is :

$\frac{13}{5}$

Putting both ratio equal

$\frac{3x + 4}{x + 4} = \frac{13}{5}$

Now, we will do cross multiple.5 will be transferred to LHS and X+4 to RHS.

$5(3x + 4) = 13(x + 4) \\ \\ 15x + 20 = 13x + 52$

Now Transferring 13x to LHS and 20 to RHS.

$15x - 13x = 52 - 20 \\ \\ 2x = 32 \\ \\ x = \frac{32}{2 }$

x = 16.

So, the age of son = 16 years.

Age of father = 3x

3(16) = 48 years

So the age of father = 48 years.

Verification

After 4 years:

$\frac{48 + 4}{16 + 4} = \frac{13}{5}$

$\frac{52}{20} = \frac{13}{5}$

$\frac{13}{5} = \frac{13}{5}$

Hence, verified.

So , present age of son is 16 and father is 48 years