The father’s age is six times his son’s age.

Question:

The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages (in year) of the

son and the father are, respectively

(a) 4 and 24                                             

(b) 5 and 30

(c) 6 and 36                                             

(d) 3 and 24

Solution:

(c)

Let x yr be the present age of father and y yr be the present age of son.

Four years hence, it has relation by given condition,

(x + 4) = 4(y + 4)

⇒                                        x-4y = 12                                                               …(i)

and                                           x = 6y                                                              …(ii)

On putting the value of x from Eq. (ii) in Eq. (i), we get

6y-4y=12

⇒                                           2y = 12

⇒                                              y = 6

When y = 6, then x = 36

Hence, present age of father is 36 yr and age of son is 6 yr.

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