Ishikha got married 9 years ago. Today her age is four third of her age at the time of marriage. At present her daughter's age is one sixth of her age. What was her daughter's age 3 years ago?

Introduction / Context:
This problem combines proportional age growth over 9 years for a mother with a present age ratio between the mother and her daughter. Once Ishikha's present age is determined, the daughter's age can be obtained easily and then adjusted to find her age 3 years ago. The problem nicely mixes fractions and time shifts.

Given Data / Assumptions:

• Ishikha got married 9 years ago.
• Her present age is 4/3 times her age at the time of marriage.
• Her daughter's present age is one sixth of Ishikha's present age.
• We must find her daughter's age 3 years ago.

Concept / Approach:
Let I be Ishikha's present age. Her age at marriage was I - 9. The relation tells us I = (4/3) * (I - 9). We solve this equation to find I. Then the daughter's current age is I / 6. Subtracting 3 years from that gives the daughter's age three years ago. The steps use proportion and simple linear equations.

Step-by-Step Solution:
Let Ishikha's present age be I years. Her age at marriage, 9 years ago, was I - 9 years. The condition says I = (4/3) * (I - 9). Multiply both sides by 3: 3I = 4(I - 9). So 3I = 4I - 36 which simplifies to -I = -36. Hence I = 36 years. Her daughter's present age is one sixth of 36, so daughter's age now = 36 / 6 = 6 years. Three years ago, daughter's age = 6 - 3 = 3 years.

Verification / Alternative check:
At marriage, Ishikha was 36 - 9 = 27 years old. Four third of 27 is (4/3) * 27 = 36, which matches her present age. The daughter being 6 years old now is indeed one sixth of 36. Three years ago, she would have been 3 years old. All conditions are satisfied, so the result is consistent.

Why Other Options Are Wrong:
A daughter aged 4 or 5 years three years ago would be 7 or 8 now, which is not one sixth of 36. Values like 1 or 2 years three years ago would make her present age 4 or 5 years, which again does not match the one sixth proportion. Only 3 years ago leads to a present age of 6, maintaining the exact ratio with Ishikha's age.

Common Pitfalls:
Mistakes often come from misinterpreting the phrase four third and writing the equation incorrectly as (3/4) instead of 4/3. Other errors include forgetting to subtract 9 to obtain the marriage age or mixing up whether to divide or multiply when using one sixth. Keeping clear symbols and carefully translating each condition minimizes such issues.

Final Answer:
Therefore, Ishikha's daughter was 3 years old three years ago.