Pipes A and B can fill a tank in 20 minutes and 30 minutes, respectively. Meanwhile, a drainpipe C can empty the tank in 60 minutes. If all three pipes are opened simultaneously, how long will it take to fill the tank?

Correct — A. Take the tank as 60 units, the LCM of 20, 30 and 60. Rates add, with the drain counted as negative.

A fills: 60 ÷ 20 = 3 units/min
B fills: 60 ÷ 30 = 2 units/min
C drains: 60 ÷ 60 = 1 unit/min

Net rate: 3 + 2 − 1 = 4 units/min
Time to fill: 60 ÷ 4 = 15 min → option (a)

Why the others are wrong

• (b)
  20 min — 20 min is pipe A's time alone. With B open too, the net rate of 4 units/min beats A's 3, so the tank fills sooner than 20 min.
• (c)
  25 min — 25 min is slower than A alone, which would need the drain to outrun B. It cannot: B adds 2 units/min and C removes only 1.
• (d)
  10 min — 10 min needs a net 6 units/min. A and B together give 5 even with the drain shut, a 12-minute fill, so the tank cannot fill in 10 min.

In pipes problems rates add, times do not. A pipe that fills a tank in t minutes does 1⁄t of it each minute, and an emptying pipe's rate is subtracted.

In fractions: 1⁄20 + 1⁄30 − 1⁄60 = 3⁄60 + 2⁄60 − 1⁄60 = 4⁄60 = 1⁄15, so the tank fills in 15 minutes. Taking the LCM as the capacity turns the same sum into whole numbers.

Key facts

• A pipe that fills a tank in t minutes fills 1⁄t of it per minute.
• Net rate = sum of filling rates − sum of emptying rates.
• Time to fill = capacity ÷ net rate.

Common traps

• Adding the drain's rate instead of subtracting it: 3 + 2 + 1 = 6 units/min gives a 10-minute fill.
• Adding times instead of rates. Two pipes together are faster than either alone, so the answer must be under A's 20 minutes.

No directly related past PYQ was found.