Seven years from now, Virat will be twice as old as Mohinder. Five years ago, Mohinder's age was one year less than two-fifths of Virat's age at that time. What is Virat's present age?

Introduction / Context:
This is a multi-step algebraic age problem involving Virat and Mohinder. We are given a future relationship between their ages and a past relationship where Mohinder's age is tied to a fraction of Virat's age at that past time. We must carefully interpret these time-based conditions to determine Virat's present age. Such problems test both algebraic manipulation and careful reading of age statements involving different time points.

Given Data / Assumptions:

- Let Virat's present age be V years and Mohinder's present age be M years.
- Seven years from now, Virat's age will be twice Mohinder's age at that time: V + 7 = 2(M + 7).
- Five years ago, Mohinder's age was one year less than two-fifths of Virat's age at that time: M − 5 = (2 / 5)(V − 5) − 1.
- All ages are in whole years.

Concept / Approach:
We translate each time-based statement into an equation involving V and M. The future condition (seven years from now) gives one linear equation, and the past condition (five years ago) gives another linear equation. Solving these two equations simultaneously yields the present ages of Virat and Mohinder. Finally, we select Virat's age as the required answer.

Step-by-Step Solution:
Step 1: From the future condition, seven years from now Virat will be twice Mohinder's age at that time: V + 7 = 2(M + 7). Step 2: Expand Step 1: V + 7 = 2M + 14 ⇒ V = 2M + 14 − 7 = 2M + 7. Step 3: From the past condition, five years ago Mohinder's age was one year less than two-fifths of Virat's age at that same time: M − 5 = (2 / 5)(V − 5) − 1. Step 4: Substitute V = 2M + 7 from Step 2 into the past condition. Step 5: Compute V − 5 = (2M + 7) − 5 = 2M + 2. Step 6: Then (2 / 5)(V − 5) = (2 / 5)(2M + 2) = (4M + 4) / 5. Step 7: The past condition becomes M − 5 = (4M + 4) / 5 − 1. Step 8: Simplify the right-hand side: (4M + 4) / 5 − 1 = (4M + 4 − 5) / 5 = (4M − 1) / 5. Step 9: Therefore, M − 5 = (4M − 1) / 5. Step 10: Multiply both sides by 5: 5(M − 5) = 4M − 1 ⇒ 5M − 25 = 4M − 1. Step 11: Rearrange: 5M − 4M = −1 + 25 ⇒ M = 24 years. Step 12: Substitute M = 24 back into V = 2M + 7 to find Virat's present age: V = 2 × 24 + 7 = 48 + 7 = 55 years.

Verification / Alternative check:
Check both conditions with V = 55 and M = 24. Seven years from now, Virat will be 55 + 7 = 62 years old and Mohinder will be 24 + 7 = 31 years old. Twice Mohinder's age at that time is 2 × 31 = 62, which matches Virat's age, satisfying the first condition. Five years ago, Virat was 55 − 5 = 50 years old and Mohinder was 24 − 5 = 19 years old. Two-fifths of Virat's age at that time is (2 / 5) × 50 = 20. One year less than that is 20 − 1 = 19, which matches Mohinder's age, satisfying the second condition. Both conditions hold exactly.

Why Other Options Are Wrong:
If Virat's present age were 51, 53, 57 or 60 years, then there would be no corresponding integer age for Mohinder that satisfies both time-based equations simultaneously. For instance, changing Virat's present age to 53 would break either the future doubling condition or the past two-fifths condition when we attempt to solve the equations. Only 55 years fits both constraints.

Common Pitfalls:
Students often misinterpret the phrase "two-fifths of Virat's age" and may apply it to Virat's present age instead of his age five years ago. Another frequent error is in algebraic manipulation, especially when dealing with fractions and subtracting 1. Carefully identifying the correct time reference for each age and simplifying step by step is crucial to avoid mistakes.

Final Answer:
Virat's present age is 55 years.