Question

five years hence , the fathers age will be three times that of his son. five years ago, father was seven times as old as his son. find their present ages

Answer 1

The answer of this question is 10, 40

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption

Present age of man be p

Also,

Present age of his son be t years

First situation :-

Man age after five years = p + 5

Son age after five years = t + 5

So,

p + 5 = 3(t + 5)

p - 3t = 10 ……………(1)

Now,

Second Situation :-

Man age before five years = p - 5

Son age before five years = t - 5

So,

p - 5 = 7(t - 5)

p - 7t = -30 ……...........(2)

Now,

Subtract (2) from (1),

4t = 40

t = 10

Now,

Substitute value of t in (1) :-

⇒ p - 3t = 10

⇒ p - 3 × 10 = 10

⇒ p = 10 + 30

⇒ p = 40

Therefore,

Present age of man = 40 years

Present age of son = 10 years