Amit's father is aged five times more than Amit. After 6 years, he would be three and a half times Amit's age. After further 9 years, how many times of Amit's age would he be?

Question

Accepted Answer

Let Amit's current age be x years.

According to the problem, Amit's father is aged five times more than Amit. This means:
Father's age = x + 5x = 6x

After 6 years:
Amit's age = x + 6
Father's age = 6x + 6

Given that after 6 years, father's age is three and a half times Amit's age:
6x + 6 = 3.5(x + 6)
6x + 6 = (7/2)(x + 6)
Multiply both sides by 2:
12x + 12 = 7x + 42
12x - 7x = 42 - 12
5x = 30
x = 6

So, Amit's current age is 6 years.
Father's current age = 6x = 36 years.

After further 9 years (which is 6 + 9 = 15 years from now):
Amit's age = 6 + 15 = 21 years
Father's age = 36 + 15 = 51 years

Ratio of father's age to Amit's age after 15 years:
51 / 21 = 17 / 7 = 2 (3/7) times

Note: The options given are 2 (3/4), 2 (1/4), 3 (2/7), and 2 (3/7). The correct ratio is 2 (3/7) times.

Rechecking the initial interpretation:
"Amit's father is aged five times more than Amit" means father's age = Amit's age + 5 times Amit's age = 6 times Amit's age.

The calculation is consistent.

Therefore, the correct answer is 2 (3/7) times.

Answer

Answer

Answer