Given:
Suresh present age = 2/5th of His father's present age
After some years,
Suresh age = 75% of his father's age
Calculation:
Suresh's present age is 2/5 of his father's present age.
S = 2/5F
After x years, Suresh's age will become 75% of his father's age at that time.
S + x = 0.75 (F + x)
We need to find by what percent the father's age will increase during this period.
Express x in terms of F
We already know S= (2/5)F
Substituting this in the second equation:
⇒ (2/5)F + x = 0.75 (F + x)
⇒ (2/5)F + x = 0.75F + 0.75x
⇒ (x − 0.75x) = 0.75F − (2/5)F
⇒ 0.25x = (15F - 8F)/20
⇒ 0.25x = (7/20)F
⇒ x = [(7/20)F] / 0.25
⇒ x = (7/5)F
The father's age increases from F to (F+x), so:
Father's age increased by = F + x = F + (7/5)F = (12/5)F
The percentage increase in the father's age is:
Percentage Increase = {[(12/5)F - F] / F} * 100
Percentage Increase = {[(7/5)F] / F} * 100 = (7/5) * 100 = 140%
∴ The correct answer is Option 3).