Two pipes can fill a tank in 12 hours and 18 hours, respectively, while a third pipe can empty it in 8 hours. How long (in hours) will it take to fill the empty tank if all three pipes are opened simultaneously?

Correct — C. Give the tank a convenient size: 72 units, the LCM of 12, 18 and 8.

Work out each pipe's rate per hour:
first pipe fills 72 ⁄ 12 = +6
second pipe fills 72 ⁄ 18 = +4
third pipe empties 72 ⁄ 8 = −9

Net rate = 6 + 4 − 9 = +1 unit per hour

Time = 72 ÷ 1 = 72 hours → option (c).

Why the others are wrong

• (a)
  36 — 36 hours means a net rate of 2 units an hour, which is 6 + 4 − 8. That treats the outlet's 8 hours as its rate instead of computing 72 ⁄ 8 = 9.
• (b)
  24 — 24 hours means a net rate of 3 units an hour. No combination of +6, +4 and −9 produces 3, so no reading of the data supports it.
• (d)
  48 — 48 hours means a net rate of 1.5 units an hour. On a 72-unit tank all three rates are whole numbers, and they add to exactly 1.

Pipe-and-cistern problems turn into plain arithmetic once the tank is given a size.

Take the LCM of the times as the capacity — 72 units here — and each pipe's rate is capacity ÷ its own time. Inlets count positive, outlets negative.

Net rate = +6 + 4 − 9 = +1, and time = capacity ÷ net rate.

The answer equalling the capacity number is a coincidence of this data, not a rule — it happens only because the net rate came out as exactly 1.

Key facts

• LCM(12, 18, 8) = 72.
• On a 72-unit tank the rates are +6, +4 and −9 units per hour.
• Time to fill = capacity ÷ net rate = 72 ÷ 1 = 72 hours.

Common traps

• Using 8 as the outlet's rate instead of 72 ⁄ 8 = 9
• Adding all three rates as positives and answering with a far shorter time

No directly related past PYQ was found.