There are two pipes used to fill a tank and when operated together, they can fill the tank in 20 minutes. If one pipe can fill the tank two and a half times as quickly as the other, then the faster pipe alone can fill the tank in:
- (a)34 min
- (b)30 min
- (c)32 min
- (d)28 min
Answer
Why
Correct — D. Work in rates, not in times.
Let the slower pipe take t minutes, so its rate is 1⁄t.
The faster pipe is two-and-a-half times as quick, so its rate is 2.5⁄t.
Together: 1⁄t + 2.5⁄t = 3.5⁄t = 1⁄20
So t = 3.5 × 20 = 70 min for the slower pipe
Faster pipe = 70 ⁄ 2.5 = 28 min → option (d).
Check: 1⁄70 + 1⁄28 = 2⁄140 + 5⁄140 = 7⁄140 = 1⁄20.
Why the others are wrong
- (a)34 min — 34 min makes the slower pipe 34 × 2.5 = 85 min, and those two together fill in 170⁄7 ≈ 24.3 min, not 20. Substituting back rejects it in one line.
- (b)30 min — 30 min pairs with a slower pipe of 75 min, and together they take 150⁄7 ≈ 21.4 min. It is the nearest miss on the list, which is exactly why it is offered.
- (c)32 min — 32 min pairs with 80 min and gives a combined time of 160⁄7 ≈ 22.9 min. Every option above 28 makes the pair too slow to finish in 20 minutes.
Concept
Pipe-and-cistern items are rate items. A pipe that fills a tank in t minutes has rate 1⁄t tanks per minute, and rates add when pipes run together.
Two and a half times as quick is a statement about rates, not times. The faster pipe's rate is 2.5 times the slower pipe's, so its time is the slower time divided by 2.5.
Reversing that — multiplying the time by 2.5 instead of dividing — turns a sound method into a wrong answer, and it also hands you the wrong pipe.
The question asks for the faster pipe. The rate algebra naturally lands on the slower pipe's 70 minutes first, so there is one more division to do after t is found.
Key facts
- If two pipes take a and b minutes alone, together they take ab ⁄ (a + b) minutes.
- A pipe that is k times as quick takes 1⁄k of the time, never k times the time.
- Here the pipes take 70 and 28 minutes alone, and 1⁄70 + 1⁄28 = 1⁄20.
Study next
Common traps
- Multiplying the slower time by 2.5 and reporting the slower pipe as the faster one
- Splitting the 20 minutes in the ratio 2.5 : 1, which averages times instead of adding rates
The identical set-up with a different multiplier is at 11 Sep 2024, 09:00, Quant Q.17 — together 15 minutes, one pipe one and a half times as fast, faster pipe wanted.
It is inverted at 26 Sep 2024, 09:00, Quant Q.21, where one pipe is four times as fast, the pair fills in 48 minutes and the slower pipe is asked for.
Related PYQs
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