🛁 Pipes & Cisterns — Advanced
5 exam question types, fully solvedThe harder pipe questions add a twist — a pipe is shut partway, a hidden leak slows things down, the tank is measured in litres, or pipes open in turns. Each twist has a clean handle once you keep working in units per hour.
Always start the same way: capacity = LCM of the times, every pipe a signed rate.
• Pipe closed / opened mid-way: “the tank fills in hours, but a pipe is shut after hours.” Count units filled while all pipes run, then units for the remaining time with the leftover pipes — add to reach the full capacity and solve for the unknown.
• Leakage: a pipe alone fills in h but with a leak takes h. The leak's draining rate , so the leak alone empties a full tank in hours.
• Litres / capacity: here the net rate is in litres per hour. If filling adds L/h and draining removes L/h and the tank still fills in h, then capacity . Find the missing pipe by back-solving this.
• Alternate opening: pipes take turns (one hour each). Treat it as a repeating block — sum one full cycle's net fill, count how many cycles fit, then finish the remainder hour by hour.
Try the twists in the simulator above: set A = 12 h, B = 15 h and close B after 3 h — capacity 60, rates +5 and +4, so 3 hours together fill 27 units and A alone needs h more: full at 9.6 h. Then switch to fill with leak (A = 6 h, leak = 10 h) and watch the net stretch the fill to 15 h.
A pipe fills a tank in 10 h, but a leak makes it 15 h. The leak alone empties it in hours.
When pipes differ only in diameter, water flow is proportional to the cross-section area, so flow ∝ d². Diameters 2, 3, 4 cm give flow ratio — turn one known fill time into the tank's capacity in units, then divide by the combined flow.
Worked (SSC CGL Tier II): three taps have diameters 2 cm, 3 cm and 4 cm; the widest tap alone fills the tank in 81 min. Flow ratio = , so capacity = 16 × 81 = 1296 units. All three together pour 4 + 9 + 16 = 29 units/min, giving min 41 s.
Worked (SSC MTS, alternate days): pipe A fills in 30 days, pipe B empties in 50 days; they open on alternate days starting with A. Capacity = LCM(30, 50) = 150 units, so A = +5/day, B = −3/day and each 2-day cycle nets +2. Trap: don't just compute 150 ÷ 2 = 75 cycles — the tank tops out mid-cycle on a fill day. After 73 cycles (146 days) it holds 146 units; on day 147 pipe A needs only 4 of its 5 units, so the tank fills on day .
Q1A pipe fills a tank in 10 minutes. Due to a leak, it now takes 15 minutes to fill. How long will the leak alone take to empty a full tank?
Q2Taps P (10 hours) and Q (12 hours) are opened together at 9 a.m. At what time should P be closed so the tank is full exactly at 3 p.m.?
Q3Three pipes fill a tank at 100, 80 and 60 litres/min while two drains empty it at 50 and 40 litres/min. If all are open, the net filling rate is:
Real exam questions — Pipes & Cisterns Advanced
5 question types · 17 solved examples from real SSC papersAdvanced pipes and cisterns: set capacity = LCM of the times, give each pipe a signed rate (fill +, drain -), then handle pipes that start late, leak, are measured in litres, or take turns in a repeating cycle.
A fills a tank in 12 hours and B in 18 hours. Both are opened at 6 a.m. At what time should B be closed so the tank is full by 4 p.m. (10 hours later)?
A pipe fills a tank in 16 hours; an outlet empties it in 24 hours. The fill pipe is opened first, and the outlet is opened 8 hours later. How long does the tank take to fill in all?
Pipes A (20 hours) and B (30 hours) fill a tank. B is opened alone for the first 10 hours, then A is also opened. Total time to fill the tank?
Pipe A (12 hours) is opened first. After 3 hours B (18 hours) is opened, and 3 hours after that C (24 hours) is opened. All stay open. Approximately when is the tank full?