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 years, of the son and the father are, respectively

(A) 4 and 24                                       

(B) 5 and 30

(C) 6 and 36                                       

(D) 3 and 24​

Answer 1

Answer: (C)

Explanation: Let the age of father be x and of son is y.

Then according to question,

x = 6y …..(i)

Four years hence age of son will be y + 4 and age of father will be x + 4

Then according to question,

x + 4 = 4 (y + 4)

x – 4y = 12 …..(ii)

Solving equations (i) and (ii) we get:

y = 6 and x = 36

hope it's helps ✌️

Answer 2

Solution :

Let the present age of son's be r years & the present age of father's be m years.

$\underline{\boldsymbol{According\:to\:the\:question\::}}}}$

$\longrightarrow\sf{m=6r.................(1)}$

$\underbrace{\bf{4\:years\:later\::}}}$

The age of son will be (r+4) years.

The age of father will be (m+4) years.

$\longrightarrow\sf{(m+4)=4(r+4)}\\\\\longrightarrow\sf{m+4=4r+16}\\\\\longrightarrow\sf{6r+4=4r+ 16\:\:[from(1)]}\\\\\longrightarrow\sf{6r-4r=16-4}}\\\\\longrightarrow\sf{2r=16-4}\\\\\longrightarrow\sf{2r=12}\\\\\longrightarrow\sf{r=\cancel{12/2}}\\\\\longrightarrow\bf{r=6\:years}$

∴ Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=6\times 6}\\\\\longrightarrow\bf{m=36\:years}$

Thus;

The present age of son's be 6 years.

The present age of father's be 36 years.

Option (c)