Present age of Jacob be ‘x’.
His son’s present age is ‘y’.
After 5 years, Age of Jacob will be x + 5
After 5 years, Age of his son will be y + 5
At that time Jacob’s age will be three times that of his son.
x + 5 = 3(y + 5)
x + 5 = 3y + 15
x – 3y = 15 – 5
x – 3y = 10 ………… (i)
5 years ago Jacob’s age was x – 5
5 years ago, age of Jacob’s son was y – 5
At that time Jacob’s age was seven times that of his son.
∴ x – 5 = 7(y – 5)
x – 5 – 7y – 35
x – 7y = -35 + 5
x – 7y = -30 ………….. (ii)
From eqn. (i),
x – 3y = 10
x = 10 + 3y
Substituting the value of ‘x’ in eqn. (ii),
x – 7y = -30
10 + 3y – 7y = -30
10 – 4y = -30
-4y = -30 – 10
-4y = -40
∴ y = \(\frac{40}{4}\)
∴ y = 10
Substituting the value of ‘y’ in
x = 10 + 3y
= 10 + 3 × 10
= 10 + 30
∴ x = 40
∴ Present age of Jacob is 40.
Present age of Jacob’s son is 10 .