Pooja, Shipra and Mounika are three sisters, and Pooja and Shipra are twins of equal age. The sum of the present ages of Pooja and Shipra is equal to the present age of Mounika. Three years earlier, the ratio of the age of Pooja to the age of Mounika was 2 : 7. What will be the age of Shipra three years hence?

Introduction / Context:
This is a classic age problem involving ratios and simple linear equations. We are told that Pooja and Shipra are twins with equal ages, that their combined age equals Mounika's present age, and that three years earlier there was a given ratio between Pooja's and Mounika's ages. Using this information, we need to determine Shipra's age three years in the future.

Given Data / Assumptions:

• Pooja and Shipra are twins, so their present ages are equal.
• The sum of the present ages of Pooja and Shipra equals Mounika's present age.
• Three years earlier, Pooja's age : Mounika's age = 2 : 7.
• We must find Shipra's age three years hence.
• All ages are measured in whole years.

Concept / Approach:
Let the present age of each twin be x years. Then Mounika's present age is 2x years, since it equals the sum of the twins' ages. We then use the ratio condition from three years earlier, when Pooja's age was x − 3 and Mounika's age was 2x − 3. Setting their ratio to 2 : 7 gives an equation in x. Solving for x gives the present age of each twin, from which we can add three years to find Shipra's age three years hence.

Step-by-Step Solution:
Let present age of Pooja = x years. Since Pooja and Shipra are twins, present age of Shipra = x years. Sum of ages of Pooja and Shipra = x + x = 2x years. Given that Mounika's present age = 2x years. Three years earlier, Pooja's age = x − 3 years. Three years earlier, Mounika's age = 2x − 3 years. The ratio (x − 3) : (2x − 3) = 2 : 7. Form the equation (x − 3) / (2x − 3) = 2 / 7. Cross multiply: 7(x − 3) = 2(2x − 3). This gives 7x − 21 = 4x − 6. So 7x − 4x = −6 + 21, which is 3x = 15. Hence x = 5. So present age of Shipra is 5 years. Shipra's age three years hence will be 5 + 3 = 8 years.

Verification / Alternative check:
Using x = 5, the present ages are: Pooja = 5, Shipra = 5 and Mounika = 10. Three years earlier, their ages were: Pooja = 2, Mounika = 7. The ratio 2 : 7 matches the given condition. Also, the sum of present ages of Pooja and Shipra is 5 + 5 = 10, which equals Mounika's present age. This confirms that the assumptions and calculations are consistent.

Why Other Options Are Wrong:
Values such as 12, 16, 18 or 21 years do not align with the derived present age of 5 years for Shipra. If Shipra were to be any of those ages three years hence, her current age would be inconsistent with both the ratio condition and the sum condition involving Mounika. Only 8 years fits both constraints.

Common Pitfalls:
A common error is to misinterpret the statement about the sum of the ages of Pooja and Shipra and to treat it as a ratio instead of an equality. Another mistake is to apply the ratio at the wrong time, using present ages instead of ages three years earlier. Always pay close attention to time shifts in age problems.

Final Answer:
Shipra's age three years hence will be 8 years.