Mathematics

Grade10

Easy

Question

# A man's age is three times that of his son and in twelve years he will be twice as old as his son would be. Find their present ages.

- Present age of man is 60 years and
Present age of son is 20 years
- B Present age of man is 45 years and
Present age of son is 15 years
- C Present age of man is 54 years and
Present age of son is 18 years
- D Present age of man is 36 years and
Present age of son is 12 years

Hint:

### In this question, we have to find the age of man and his son. Firstly the man age is three times its son . Hence twelve years , the man age is twice old as his son age. Consider them as variable and make the equation for solution.

## The correct answer is: D Present age of man is 36 years and

Present age of son is 12 years

### Here we have to find that age of man and his son,

Firstly , it is given at first the man age is three times his son .

Lets father be a and son be b,

So , b = 3a ---(1)

And after twelve years ,

man age is twice age to his son , so we can write,

b+12 = 2(a+12) [we add 12 in both sides because it is after 12 years so both age ages are added by 12]

b + 12 = 2a + 24

3a + 12 = 2a + 24( using (1))

3a – 2a = 24 - 12

a =12

put value of a in eq (1),

b = 3a

b = 3 x 12

b = 36

Therefore , The present age of man and his son is 12 and 36

The correct answer is Present age of man is 36 years and Present age of son is 12 years.

Or,

Let the present age of son be x years

As per question the present age of father is three times

then present age of father is 3x

As per question after 12 years the age of father will be twice the age of son

3x+12=2(x+12)

⇒3x+12=2x+24

⇒3x−2x=24−12

⇒x=12

Then present age of son is 12 years

So present age of father =3×12=36 years

In this question, we have to make equation on the given date about ages. Consider all the character in similar ages question be some variable and make the equation on given details.