The sum of the ages of Anushka, Kajal and Charulatha is 57 years. Kajal is three times as old as Anushka and Charulatha is 12 years older than Anushka. What are the respective present ages of Anushka, Kajal and Charulatha?

Introduction / Context:
This is a direct linear equations problem involving three people whose ages are linked by simple multiplicative and additive relations. We are given the total of their ages and two separate relationships involving Anushka's age. Solving these relations gives the individual ages exactly.

Given Data / Assumptions:

• The sum of the present ages of Anushka, Kajal and Charulatha is 57 years.
• Kajal is three times as old as Anushka.
• Charulatha is 12 years older than Anushka.
• We must find the present ages of Anushka, Kajal and Charulatha.

Concept / Approach:
Let Anushka's age be A years. Then Kajal's age is 3A and Charulatha's age is A + 12. Using the total age equation A + 3A + (A + 12) = 57, we solve for A. Once A is known, we immediately obtain Kajal's and Charulatha's ages and match them with the correct option.

Step-by-Step Solution:
Let Anushka's present age be A years. Then Kajal's present age = 3A years. Charulatha's present age = A + 12 years. The sum of their ages is A + 3A + (A + 12) = 57. Simplify: A + 3A + A + 12 = 57 gives 5A + 12 = 57. Subtract 12 from both sides: 5A = 45. Hence A = 45 / 5 = 9. So Anushka's age is 9 years, Kajal's age = 3 * 9 = 27 years, and Charulatha's age = 9 + 12 = 21 years.

Verification / Alternative check:
Check the total: 9 + 27 + 21 = 57, which matches the given sum. Check the relations: Kajal is three times as old as Anushka since 27 = 3 * 9, and Charulatha is 12 years older because 21 = 9 + 12. Both conditions are satisfied, confirming that the ages 9, 27 and 21 are correct.

Why Other Options Are Wrong:
Option 27, 9, 21 does not satisfy the relation that Kajal is three times Anushka's age. Option 9, 21, 27 reverses the roles of Kajal and Charulatha. Option 21, 27, 9 puts Anushka as the oldest, which contradicts the conditions. The set 15, 27, 15 sums to 57 but fails both the three times relation and the 12 year difference. Only 9, 27, 21 satisfies all the given statements simultaneously.

Common Pitfalls:
A common mistake is to misassign the multiplication factor, for example setting A = 3K instead of K = 3A. Another error is forgetting to include the +12 for Charulatha when writing the total equation. Defining a single variable and expressing all other ages in terms of it is the safest way to approach such problems.

Final Answer:
Thus, the respective ages of Anushka, Kajal and Charulatha are 9, 27 and 21 years.