In a company, the average salary of 5 engineers is Rs. 60,000. If one engineer leaves and the average salary becomes Rs. 58,000, what was the salary of the engineer who left?

Correct — B. Work with totals, not averages.

Total of 5 salaries: 5 × 60,000 = 3,00,000
Total of the 4 who stay: 4 × 58,000 = 2,32,000
Salary of the leaver: 3,00,000 − 2,32,000 = ₹68,000 → option (b)

Why the others are wrong

• (a)
  Rs. 70,000 — ₹70,000 spreads the ₹2,000 fall over all five: 60,000 + 5 × 2,000. Only the four who stay carry the new average. Check: 2,30,000 left over four is ₹57,500.
• (c)
  Rs. 64,000 — ₹64,000 leaves the other four with 2,36,000, an average of ₹59,000. The stem says the average became ₹58,000.
• (d)
  Rs. 62,000 — ₹62,000 adds the ₹2,000 fall only once. The other four would total 2,38,000, an average of ₹59,500, not ₹58,000.

An average hides a total: total = average × count. When one member leaves, compare the totals before and after. The difference is the member who left.

Shortcut: the leaver = old average + (members remaining × fall in average) = 60,000 + 4 × 2,000 = 68,000. The leaver earned above the old average, which is why the average fell.

Key facts

• Sum = average × number of items.
• Value removed = old sum − new sum.
• If removing one value lowers the average by d, that value = old average + (remaining count × d).

Common traps

• Multiplying the ₹2,000 fall by 5, the original count, instead of 4. That gives ₹70,000.
• Adding the ₹2,000 fall to the old average once, 60,000 + 2,000 = ₹62,000, instead of once for each of the four who stay.

No directly related past PYQ was found.