5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is (a) 45 years (b) 50 years (c) 47 years (d) 40 years

Home » 5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is (a) 45 years (b) 50 years (c) 47 years (d) 40 years

5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is
(a) 45 years
(b) 50 years
(c) 47 years
(d) 40 years

5 years hence, the age of a man shall be 3 times the age of his son while 5 years earlier the age of the man was 7 times the age of his son. The present age of the man is
(a) 45 years
(b) 50 years
(c) 47 years
(d) 40 years

Answer: (d) 40 years

Solution:
Suppose the present age of the man be $\mathrm{x}$ years.
And his son’s present age be $y$ years.
5 years later:
$\begin{array}{l} (x+5)=3(y+5) \\ \Rightarrow x+5=3 y+15 \\ \Rightarrow x-3 y=10\dots \dots(i) \end{array}$
5 years ago:
$\begin{array}{l} (x-5)=7(y-5) \\ \Rightarrow x-5=7 y-35 \\ \Rightarrow x-7 y=-30\dots \dots(ii) \end{array}$
On subtracting equation(i) from equation(ii), we obtain:
$-4 y=-40 \Rightarrow y=10$
On substituting $\mathrm{y}=10$ in equation(i), we have:
$x-3 \times 10=10 \Rightarrow x-30=10 \Rightarrow x=(10+30)=40$ years
As a result, the man’s present age is 40 years.