Seven years ago the age of Sahil was equal to the present age of Nihal. The sum of the age of Sahil 5 years ago and the age of Nihal 6 years later is 58 years. If Ruchi is 4 years older than Sahil at present, what will be the age of Ruchi after 10 years?

Introduction / Context:
This is a multi person age problem involving Sahil, Nihal, and Ruchi. The relationships among their ages are described at different points in time, both in the past and in the future. Using these relationships, we first find the present ages of Sahil and Nihal and then determine Ruchi's age in the future. Such questions appear frequently in aptitude tests and require setting up simple linear equations.

Given Data / Assumptions:
- Seven years ago, the age of Sahil was equal to the present age of Nihal.
- The sum of the age of Sahil 5 years ago and the age of Nihal 6 years later is 58 years.
- Ruchi is currently 4 years older than Sahil.
- All ages are in complete years.
- We must find Ruchi's age after 10 years from now.

Concept / Approach:
We assign variables to the present ages of Sahil and Nihal and then translate each statement into an equation. The first statement connects Sahil's age seven years ago with Nihal's current age. The second statement connects two different times for Sahil and Nihal and gives a sum. Once we solve these equations to find Sahil's age, we can add 4 years to find Ruchi's present age and then add 10 more years to find Ruchi's age after 10 years.

Step-by-Step Solution:
Step 1: Let the present age of Sahil be S years and the present age of Nihal be N years.Step 2: Seven years ago, Sahil was S - 7 years old. The problem states that S - 7 equals the present age of Nihal, so S - 7 = N.Step 3: Five years ago, Sahil's age was S - 5. Six years from now, Nihal's age will be N + 6. The sum of these two ages is given as 58 years, so S - 5 + N + 6 = 58.Step 4: Simplify the sum equation to S + N + 1 = 58, which gives S + N = 57.Step 5: From S - 7 = N, we have N = S - 7. Substitute this into S + N = 57 to get S + (S - 7) = 57.Step 6: Simplify: 2S - 7 = 57, so 2S = 64 and S = 32 years. Thus Sahil is 32 years old now and Nihal is N = S - 7 = 25 years old.Step 7: Ruchi is 4 years older than Sahil, so her present age is 32 + 4 = 36 years. After 10 years, Ruchi will be 36 + 10 = 46 years old.

Verification / Alternative check:
Seven years ago, Sahil was 32 - 7 = 25 years old, which matches Nihal's present age of 25 years, so the first condition is satisfied. Five years ago, Sahil was 27 years old, and six years from now Nihal will be 31 years old. Their sum 27 + 31 equals 58, which matches the given sum. Finally, Ruchi being 36 years old now and 46 years old after 10 years is consistent with the information. All conditions are satisfied.

Why Other Options Are Wrong:
If Ruchi were 38, 42, 36, or 40 years old after 10 years, her present age would be 28, 32, 26, or 30 years respectively, which would lead to inconsistent ages for Sahil and Nihal when the conditions are checked. These inconsistent values would not satisfy both the seven year and the sum conditions. Therefore, those options cannot be correct.

Common Pitfalls:
Many learners misread the time references in the question and mix up ages 5 years ago, 6 years later, and 7 years ago. Another common mistake is to assume that the difference between Sahil and Nihal's ages changes over time, whereas it actually remains constant. Setting up the equations carefully using the correct time frames is crucial for reaching the right solution.

Final Answer:
Ruchi will be 46 years old after 10 years.