A pipe can fill an overhead tank in 12 hours. But due to a leak at the bottom, it is filled in 18 hours. If the tank is full, how much time will the leak take to empty it?
- (a)36 hours
- (b)7.2 hours
- (c)63 hours
- (d)3.6 hours
Answer
Why
Correct — A. Work in tank-per-hour rates and treat the leak as a negative rate.
Pipe alone fills in 12 h → rate = 1⁄12 tank per hour
Pipe with the leak fills in 18 h → net rate = 1⁄18 tank per hour
Leak's rate = 1⁄12 − 1⁄18
over the LCM 36: 3⁄36 − 2⁄36 = 1⁄36 tank per hour
Draining 1⁄36 of the tank each hour, the leak empties a full tank in 36 hours → option (a).
Why the others are wrong
- (b)7.2 hours — 7.2 is (12 × 18) ⁄ (12 + 18), the formula for two taps filling together. The leak works against the pipe, so the rates subtract rather than add.
- (c)63 hours — 63 is the digits of 36 reversed and matches no rate here. The subtraction 1⁄12 − 1⁄18 gives exactly 1⁄36, fixing the emptying time at 36 hours.
- (d)3.6 hours — 3.6 is 36 with a misplaced decimal. A leak draining the whole tank in 3.6 hours would outpace the 12-hour pipe outright and the tank would never fill at all.
Concept
Pipes and cisterns is work-and-time with a sign attached. Convert every time into a rate: a job finished in t hours proceeds at 1⁄t of the job per hour.
Inlets count positive, outlets negative, and rates acting at the same time simply add:
1⁄12 + (−1⁄L) = 1⁄18.
Solving that for the negative term gives the leak's own rate, and inverting it gives the time the leak needs alone.
Times themselves are never added or subtracted — only rates are.
The phrase 'due to a leak at the bottom' is what makes 18 hours a net figure rather than a second independent pipe, and it is the whole reason the two rates subtract.
Key facts
- A pipe filling a tank in t hours works at 1⁄t of the tank per hour.
- Simultaneous rates add, with an emptying pipe counted as negative.
- Here 1⁄12 − 1⁄18 = 1⁄36, so the leak alone empties a full tank in 36 hours.
- The standard shortcut is ab ⁄ (b − a) = (12 × 18) ⁄ 6 = 36 hours.
Study next
Common traps
- Adding the rates instead of subtracting, which returns the two-inlet figure of 7.2 hours.
- Subtracting the times, 18 − 12 = 6, and calling six hours the leak's emptying time.
- Inverting only one of the two fractions before combining them.
SSC states the clean filling time and the delayed one and asks for the leak, which is always the difference of two reciprocals. The same subtract-the-rates idea drives Quant Q.6 of this shift, where a policeman's speed closes a 600-metre gap on a running thief.
Related PYQs
No directly related past PYQ was found.