Question

Q13) A man is three times as old as his son. After 5 years, the ratio of their
ages will be 5:2. Find their present ages.
below.​

Answer 1

Let the present age of the son be x years.

Let the present age of the man be 3x years.

Age of the son after 5 years = (x+5) years.

Age of the man after 5 years = (3x+5) years.

Given:

After 5 years, the ratio of their ages will be 5:2.

To find:

The present ages of the son and the man.

Equation:

$\frac{3x+5}{x+5}=\frac{5}{2}$

2×(3x+5) = 5×(x+5)

6x+10 = 5x+25

6x-5x = 25-10

x = 15 years.

Answer:

Present age of the son is 15 years.

Present age of man = 3x

                                 = 3×15

                                 = 45 years.

Answer 2

Answer

Given,

• A man is three times as old as his son .
• after 5 year the ratio of their ages will be 5:2 .

To find,

• their present age .

So,

• let the present age of be x yrs .
• and the father age be 3x yrs .

after 5 years

• age of son = (x+5)
• age of father (3x+5)

Now ,

we know that ;

$= > \frac{3x + 5}{x + 5} = \frac{5}{2}$

by solving this we get ;

$= > 2(3x + 5) = 5(x + 5) \\ = > 6x + 10 = 5x + 25 \\ = > 6x - 5x = 25 - 10 \\ = > = 15yrs$

the present age of son is 15 years .

The present age of father = 3x = 3×15= 45 yrs

The present age of father is 45yrs and the age of son is 15yrs .