Four years ago, the ratio of (1/2 of Anita's age at that time) to (4 times Bablu's age at that time) was 5:12. Eight years from now, half of Anita's age will be 2 years less than Bablu's age at that time. What is Bablu's present age (in years)?

Introduction:
This ages question combines a past ratio condition with a future comparison involving “half of age.” It tests careful time shifting (4 years ago and 8 years hence) and forming equations from ratios. The best method is to let present ages be variables, translate both conditions into equations, and solve systematically.

Given Data / Assumptions:

• Let Anita's present age = A
• Let Bablu's present age = B
• 4 years ago: ratio of (0.5 of Anita's age) to (4 times Bablu's age) was 5:12
• 8 years hence: 0.5(Anita's age) is 2 years less than Bablu's age

Concept / Approach:
Convert the ratio into an equation by cross-multiplication. Convert the future “less than by 2 years” into a direct equality. Solve the two equations to get B.

Step-by-Step Solution:
Ages 4 years ago: Anita = A - 4, Bablu = B - 4Ratio condition: (0.5(A - 4)) : (4(B - 4)) = 5 : 12So (0.5(A - 4)) / (4(B - 4)) = 5/12(A - 4) / (8(B - 4)) = 5/12Cross-multiply: 12(A - 4) = 40(B - 4)Simplify: 3(A - 4) = 10(B - 4) => 3A = 10B - 28Future condition (8 years hence): 0.5(A + 8) is 2 less than (B + 8)0.5(A + 8) = (B + 8) - 2 => 0.5A + 4 = B + 6So 0.5A = B + 2 => A = 2B + 4Substitute: 3(2B + 4) = 10B - 286B + 12 = 10B - 28 => 40 = 4B => B = 10

Verification / Alternative check:
If B=10, then A=2B+4=24. Check 4 years ago: Anita 20, Bablu 6. 0.5*20=10 and 4*6=24, ratio 10:24 = 5:12 correct. Check 8 years hence: Anita 32, half is 16; Bablu 18; 16 is 2 less than 18, correct.

Why Other Options Are Wrong:
9, 12, 15, 24: do not satisfy both the past ratio equation and the future half-age difference simultaneously.

Common Pitfalls:
Forgetting the multiplier 4 on Bablu's age in the ratio.Misreading “less than by 2” and adding 2 instead of subtracting.Applying the 4-year shift to only one person.

Final Answer:
10 years