Question

Akbar will turn 50 when his son Jehangir turns 18. What will be Akbar’s age when it will be exactly 5 times that of Jehangir?

• A. 36
• B. 40
• C. 44
• D. 48

Hint:

Use age difference to reduce the number of variables. Set up equations using future condition and solve by substitution.

Answer 1

The Correct Option is B

Step 1: Let current ages be:
Let Akbar's present age be \( A \), and Jehangir's present age be \( J \).
We're told:
When Akbar is 50, Jehangir is 18.
So, the difference in their ages is: \[ A - J = 50 - 18 = 32 \] Step 2: Let after \( x \) years, Akbar is 5 times Jehangir's age:
So: \[ A + x = 5(J + x) \] Step 3: Substitute \( A = J + 32 \):
\[ (J + 32) + x = 5(J + x) \] Step 4: Expand and solve:
\[ J + 32 + x = 5J + 5x \] \[ 32 = 4J + 4x \Rightarrow 8 = J + x \Rightarrow x = 8 - J \] Step 5: Back substitute \( J \):
We already know \( A = J + 32 \), so try integer values of \( J \) such that both Akbar and Jehangir are integers. Try \( J = 10 \Rightarrow x = 8 - 10 = -2 \) (not valid)
Try \( J = 6 \Rightarrow x = 8 - 6 = 2 \) Now check: \[ A = J + 32 = 6 + 32 = 38
\text{Akbar’s age after 2 years} = 40,
\text{Jehangir’s age after 2 years} = 8
\Rightarrow \frac{40}{8} = 5 \quad \] % Final Answer \[ \boxed{40} \]