QUESTION 5 The ages of Mohit and Amit differ by 30 years.

Let Amit's present age be x years. Then Mohit's present age is (x + 30) years since they differ by 30 years. After 5 years, Amit will be (x + 5) and Mohit will be (x + 35). Given that Mohit is 6 times as old as Amit after 5 years: x + 35 = 6(x + 5), which simplifies to x + 35 = 6x + 30, giving x = 7. Therefore, Amit's present age is 7 years.

Step-by-step Derivation:
Step 1: Define variables.

• Let Amit's present age = x years
• Mohit's present age = (x + 30) years (since they differ by 30 years)

Step 2: Set up equation for 5 years later.

• Amit's age after 5 years = x + 5
• Mohit's age after 5 years = x + 35
• Condition: Mohit is 6 times as old as Amit
• Equation: x + 35 = 6(x + 5)

Step 3: Solve for x.

• x + 35 = 6x + 30
• 35 - 30 = 6x - x
• 5 = 5x
• x = 1

Wait, let me recalculate:

• x + 35 = 6(x + 5)
• x + 35 = 6x + 30
• 35 - 30 = 6x - x
• 5 = 5x
• x = 1

Step 4: Verify with x = 1.

• Present age of Amit = 1 year
• Present age of Mohit = 31 years
• Difference = 30 years ✓
• After 5 years: Amit = 6, Mohit = 36
• Is 36 = 6 × 6? Yes, 36 = 36 ✓

Actually, the calculation shows x = 1, but let me check option B (7 years):

• Present age of Amit = 7 years
• Present age of Mohit = 37 years
• Difference = 30 years ✓
• After 5 years: Amit = 12, Mohit = 42
• Is 42 = 6 × 12? No, 6 × 12 = 72 ✗

The correct answer is actually A (1 year). Rechecking my initial response: x = 1 satisfies both conditions.