Three years from now, the age of Dharitri will be eight years less than twice the age of Eunice at that time. The sum of their present ages is 61 years. What is the present age, in years, of Dharitri?

Introduction / Context:
This age problem uses a relationship between future ages and the current sum of ages. It illustrates how to interpret statements like “eight years less than twice the age” and translate them into algebraic equations. Such problems often appear in reasoning sections to evaluate your skill in forming and solving simultaneous linear equations.

Given Data / Assumptions:

• Three years from now, Dharitri age will be eight years less than twice Eunice age at that time.
• The sum of their present ages is 61 years.
• We need to find the present age of Dharitri.
• Ages are in years and are positive.

Concept / Approach:
We start by assigning variables to the present ages of Dharitri and Eunice. Then we write expressions for their ages three years in the future. The phrase “eight years less than twice” is carefully translated into an equation involving these future ages. Combined with the equation for the present sum of ages, this gives a system of two equations in two unknowns. Solving this system yields the present ages, from which we extract the required value.

Step-by-Step Solution:
Step 1: Let the present age of Dharitri be D years and the present age of Eunice be E years. Step 2: Three years from now, Dharitri age will be D + 3 years. Step 3: Three years from now, Eunice age will be E + 3 years. Step 4: The statement says that in three years, Dharitri age will be eight years less than twice Eunice age at that time. This gives the equation D + 3 = 2 * (E + 3) - 8. Step 5: Expand the right side: D + 3 = 2E + 6 - 8 = 2E - 2. Step 6: So we have the first equation: D + 3 = 2E - 2. Step 7: We also know that the sum of their present ages is 61 years, so D + E = 61. This is the second equation. Step 8: From D + 3 = 2E - 2, rearrange to get D = 2E - 5. Step 9: Substitute D = 2E - 5 into D + E = 61 to get (2E - 5) + E = 61. Step 10: Simplify: 3E - 5 = 61, so 3E = 66 and E = 22. Step 11: Substitute E = 22 into D = 2E - 5 to get D = 2 * 22 - 5 = 44 - 5 = 39. Step 12: Therefore, Dharitri present age is 39 years.

Verification / Alternative check:
Check the conditions with D = 39 and E = 22. The sum of present ages is 39 + 22 = 61 years, which matches the given sum. Three years from now, Dharitri will be 42 years old and Eunice will be 25 years old. Twice Eunice age at that time is 2 * 25 = 50, and eight years less than this is 50 - 8 = 42, which equals Dharitri age after three years. Both statements are satisfied, confirming that the solution is correct.

Why Other Options Are Wrong:
Option A (41 years) leads to an incorrect sum or fails the future age relation when Eunice corresponding age is calculated.
Option C (36 years) does not produce 61 as the total present age when combined with a consistent age of Eunice that satisfies the future condition.
Option D (43 years) similarly fails either the future relationship or the present age sum requirement.

Common Pitfalls:
A common error is misinterpreting the phrase “eight years less than twice Eunice age” and writing D + 3 = 2E + 3 - 8 instead of correctly considering both future ages. Another mistake is to forget to increment both ages by 3 when moving to the future time. Writing each step clearly and using separate symbols for present and future ages helps avoid confusion.

Final Answer:
The present age of Dharitri is 39 years.