The present age of Rakhi is twelve times the present age of her daughter Anubha. If Anubha is 3 years old now, what was the age of Rakhi, in years, two years ago?

Introduction / Context:
This is a straightforward ages question that relates the present age of a mother to the present age of her daughter by a simple multiple. It then asks for the mother age two years in the past. Problems like this are commonly used to introduce learners to the idea of proportional relationships in age based questions.

Given Data / Assumptions:

• Rakhi present age is twelve times the present age of her daughter Anubha.
• Anubha present age is 3 years.
• We need to find Rakhi age two years ago.
• Ages are in years and non negative.

Concept / Approach:
We first calculate Rakhi present age by multiplying Anubha age by the given factor of twelve. Then, since two years ago is in the past, we subtract two years from Rakhi present age to find the required value. This is a direct application of the idea that present ages are related by a constant multiple, and time shifts apply equally to both people, although the question here only asks for Rakhi past age.

Step-by-Step Solution:
Step 1: Anubha present age is 3 years. Step 2: Rakhi present age is given as twelve times the age of Anubha. Step 3: So Rakhi present age is 12 * 3 = 36 years. Step 4: We are asked for Rakhi age two years ago. Step 5: Two years ago, her age would have been 36 - 2 = 34 years. Step 6: Therefore, Rakhi age two years earlier was 34 years.

Verification / Alternative check:
We can check quickly by thinking forwards. If Rakhi was 34 years old two years ago, then adding two years gives 36 years as her present age. Anubha is 3 years old now, and 12 times 3 is indeed 36, matching the description that Rakhi present age is twelve times Anubha present age. This confirms the correctness of the answer.

Why Other Options Are Wrong:
Option A (20 years) is far too small; adding two years gives a present age of 22 which is not twelve times 3.
Option C (30 years) would make Rakhi 32 years old now, which is not equal to 36 years, so the relation fails.
Option D (36 years) represents Rakhi present age, not her age two years ago, so it does not answer the question asked.

Common Pitfalls:
Some learners misread the question and report the present age instead of the age two years ago. Others may confuse which age needs to be multiplied or forget to subtract the two years. Always pay attention to whether the question is about present, past or future age, and double check that you have applied the time shift in the correct direction.

Final Answer:
Rakhi age two years earlier was 34 years.