Question

The ratio of the ages of father and son at present is 6: 1. After 5 years the ratio will become 7:2. Find the present age of the son?​

Answer 1

Answer:

The present age of the son is 5 years.

Step-by-step-explanation:

We have given that,

The ratio of the present ages of father and son is 6 : 1.

Let the common multiple be x.

∴ Father's present age = 6x years

And son's present age = x years

Now,

After 5 years, father's age = ( 6x + 5 ) years

And after 5 years, son's age = ( x + 5 ) years

From the given condition,

$\displaystyle{\sf\:\dfrac{(\:6x\:+\:5\:)}{(\:x\:+\:5\:)}\:=\:\dfrac{7}{2}}$

$\displaystyle{\implies\sf\:2\:\times\:(\:6x\:+\:5\:)\:=\:7\:\times\:(\:x\:+\:5\:)}$

$\displaystyle{\implies\sf\:12x\:+\:10\:=\:7x\:+\:35}$

$\displaystyle{\implies\sf\:12x\:-\:7x\:=\:35\:-\:10}$

$\displaystyle{\implies\sf\:5x\:=\ 25}$

$\displaystyle{\implies\sf\:x\:=\:\cancel{\dfrac{25}{5}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:5\:}}}}$

∴ The present age of the son is 5 years.

Answer 2

Given :-

Ratio of ages of father son at present is 6: 1. After 5 years the ratio will become 7:2

Need to find :-

The present age of the son?​

Solution :-

Let the ages of father be 6y

Son age be y

After 5 years

$\sf \dfrac{6y + 5}{y + 5} = \dfrac{7}{2}$

By cross multiplication

7(y + 5) = 2(6y + 5)

7y + 35 = 12y + 10

7y - 12y = 10 - 35

-5y = -25

5y = 25

y = 25/5

y = 5

Age of son is 5 years