Barrack Water Tank: Tanker Call or Leak Repair?
At the new 180-inmate barrack of a district jail, the overhead tank holds 6,000 litres. On 15 August the tank is one-fourth full at 06:00. The supply line runs at 40 litres per minute. From 06:00 to 10:00 a distribution line draws 15 litres per minute for washing and drinking. At 08:00 a joint in the supply line begins leaking at 5 litres per minute; the maintenance team can repair it only at 10:00, when the distribution line is shut for cleaning. The supply continues at 40 litres per minute all day. The evening meal needs 20 litres per inmate for 180 inmates, drawn between 17:00 and 18:00. The warden wants the tank full by 13:00 and also wants a reserve of at least 1,500 litres after the evening draw. A tanker of 2,000 litres can be called at 11:00 at 45 minutes' notice. Decide whether the tanker is needed and whether the leak should be repaired on priority.
1. Calculate when, if at all, the tank becomes full between 06:00 and 10:00, and state the tank level at 10:00.
Read the worked answer
Initial level = ¼ × 6,000 = 1,500 L.
06:00–08:00: inflow 40 L/min, draw 15 L/min, no leak yet. Net = 25 L/min. Gain = 25 × 120 = 3,000 L. Level at 08:00 = 4,500 L.
08:00–10:00: inflow 40, draw 15, leak 5. Net = 20 L/min. The gap to full is 6,000 − 4,500 = 1,500 L. Time = 1,500 ÷ 20 = 75 minutes. So the tank is full at 09:15. It remains full until 10:00 and overflows. Thus the level at 10:00 is 6,000 L.
2. Assume the leak is repaired at 10:00. Calculate the reserve after the evening draw at 18:00 and decide whether the 1,500-litre reserve condition is met. Does the leak change this answer while the supply is running?
Read the worked answer
At 10:00 the tank is full: 6,000 L. From 10:00 to 17:00 there is no distribution draw, and supply (40 L/min) exceeds the leak (5 L/min), so the tank stays full and the excess overflows. The leak wastes water but does not lower the tank level while the supply is on.
Evening draw = 180 × 20 = 3,600 L. Reserve = 6,000 − 3,600 = 2,400 L. This is 900 L above the 1,500 L minimum, so the tanker is not needed on these figures.
The leak still matters: it wastes 5 × 60 = 300 L/hour, or 2,100 L over seven hours. If the supply fails, the leak would drain the reserve at 5 L/min; the 900 L cushion above the minimum would last 180 minutes. So repair is justified for resilience, but it does not change today's arithmetic.
3. The warden proposes cancelling the tanker and using the ₹1,200 saved to repair the leak. What additional checks should be made before deciding, and what would make you keep the tanker on standby?
Read the worked answer
Check four things: (i) the actual per-inmate evening draw may exceed 20 L; (ii) whether a fire or emergency reserve is separately required; (iii) how often and for how long the supply fails; (iv) the repair cost versus 2,100 L of waste and the ₹1,200 tanker cost.
If a supply failure longer than about three hours is likely during the evening peak, the 2,400 L reserve could fall below the 1,500 L floor after the meal draw. In that case keep the tanker on standby. If supply is reliable and the leak is repaired the same day, cancel the tanker. The decision is a risk comparison, not just today's tank-level calculation.