When Swetha got married to Sudeer, Swetha's age was 3/4 of her husband's age. After 12 years, Swetha's age became 5/6 of her husband's age. What was Swetha's age at the time of marriage (in years)?

Introduction:
This ages problem involves fractional ratios at two different times: at marriage and 12 years later. The skill tested is converting fraction-based age relations into equations and handling the time shift correctly. Since both Swetha and Sudeer age by the same 12 years, we can set up a clean equation using their marriage-age relationship and the later ratio condition.

Given Data / Assumptions:

• Let Swetha's age at marriage = S
• Let Sudeer's age at marriage = H
• At marriage: S = (3/4) * H
• After 12 years: S + 12 = (5/6) * (H + 12)
• We need S

Concept / Approach:
Use the first relation to express H in terms of S, then substitute into the second equation and solve for S.

Step-by-Step Solution:
From S = (3/4)H, we get H = (4/3)SAfter 12 years condition: S + 12 = (5/6)(H + 12)Substitute H: S + 12 = (5/6)((4/3)S + 12)Multiply both sides by 6: 6S + 72 = 5((4/3)S + 12)Expand: 6S + 72 = (20/3)S + 60Multiply by 3: 18S + 216 = 20S + 180216 - 180 = 20S - 18S36 = 2S => S = 18

Verification / Alternative check:
If S=18, then H=(4/3)*18=24. After 12 years: Swetha 30, Sudeer 36, and 30/36 = 5/6. At marriage: 18/24 = 3/4. Both match perfectly.

Why Other Options Are Wrong:
17, 21, 23, 20: do not satisfy both fraction ratios simultaneously when 12 years are added to both ages.

Common Pitfalls:
Applying the 12-year shift to only one person.Using 3/4 and 5/6 as differences instead of ratios.Forgetting to rearrange H in terms of S before substitution.

Final Answer:
18 years