The average salary of 40 workers in a factory is Rs. 24,000. If the salary of a supervisor is added, the average rises to Rs. 24,500. What is the supervisor’s salary?

Correct — C. Average × count gives the total, so compare the salary totals before and after the supervisor joins.

Total for 40 workers: 40 × 24,000 = Rs. 9,60,000
Total for 41 people: 41 × 24,500 = Rs. 10,04,500
Supervisor = 10,04,500 − 9,60,000 = Rs. 44,500 → option (c)

Shortcut: old average + 41 × rise = 24,000 + 41 × 500 = 24,000 + 20,500 = 44,500.

Why the others are wrong

• (a)
  Rs. 44,000 — Rs. 44,000 is 24,000 + 40 × 500, which spreads the rise over 40 people. The new average covers 41, the supervisor included, so the extra is 20,500.
• (b)
  Rs. 54,000 — Rs. 54,000 would make the 41-person total Rs. 10,14,000, an average of about Rs. 24,732, not Rs. 24,500.
• (d)
  Rs. 54,500 — Rs. 54,500 makes the total Rs. 10,14,500, and 10,14,500 ÷ 41 ≈ 24,744, above the stated Rs. 24,500 average.

An average hides a total: total = average × count. When one person joins, the rise in the total is exactly that person's value.

The shortcut reads it another way. The newcomer first matches the old average, then supplies the rise for everyone now in the group: new value = old average + new count × rise.

The new count is 41, not 40, because the supervisor is inside the new average.

Key facts

• Total = average × count: 40 × 24,000 = 9,60,000.
• If one member joins and the average rises by d, the newcomer's value = old average + (new count) × d.
• If the average does not change, the newcomer's value equals the old average.

Common traps

• Multiplying the rise by 40 instead of 41, which gives Rs. 44,000.
• Stopping at 24,500 − 24,000 = 500: that is the rise per head, not the salary.

No directly related past PYQ was found.