The average weight of 30 students is 60 kg. If one student is removed, the average drops to 59.5 kg. What is the weight of the removed student?

Correct — A. Compare the group's total before and after.

Total of 30: 30 × 60 = 1800 kg
Total of 29: 29 × 59.5 = 1725.5 kg
Removed student: 1800 − 1725.5 = 74.5 kg → option (a)

Shortcut: the 29 who remain are 0.5 kg each below 60, a 14.5 kg shortfall.
So the removed student was 14.5 kg above 60: 60 + 14.5 = 74.5 kg.

Why the others are wrong

• (b)
  84.5 kg — 84.5 kg is 10 kg too heavy. Removing it leaves 1715.5 kg for 29 students, an average of about 59.16 kg, not 59.5 kg.
• (c)
  70.5 kg — 70.5 kg is 4 kg too light. Removing it leaves 1729.5 kg for 29 students, an average of about 59.64 kg, not 59.5 kg.
• (d)
  16.5 kg — 16.5 kg is below the 60 kg average, so removing it would raise the average, to 1783.5 ÷ 29 = 61.5 kg. The average fell, so the student was heavier than 60 kg.

An average question is a total question in disguise. Average × count gives the total, and any change to the group shows up as a change in the total.

When one member leaves, the value removed is the old total minus the new total. If the average drops, the member who left was above the old average.

Key facts

• Total = average × number of items.
• Value removed = old total − new total.
• If removing one value lowers the average, that value was above the old average.

Common traps

• Mixing the two shortcuts, as in 60 + 30 × 0.5 = 75 kg. Pair the old average with the 29 who remain, or the new average with the original 30.
• Multiplying the new average by 30 instead of 29. The new average belongs to the 29 students left.

No directly related past PYQ was found.