A year ago Akash's father's age was 9 times that of Akash. After 3 years his father's age will be 5 times that of his age. How old will Akash be next year?

Let's assume Akash's father's age 1 year ago is AF and Akash's age 1 year ago is A.

A year ago Akash's father's age was 9 times that of Akash.

AF = $$9 \times A$$    Eq.(1)

After 3 years his father's age will be 5 times that of his age.

$$AF + 4 = 5 \times (A + 4)$$

AF + 4 = 5A + 20

AF = 5A + 16

Put the value of Eq.(1) here.

9A = 5A + 16

4A = 16

A = 4 (Akash's age 1 year ago.)

So Akash's age 1 year hence will be 6 years.

Hence, option d is the correct answer.