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Question

It takes pump (A) $$4$$ hours to empty a swimming pool. It takes pump (B) $$6$$ hours to empty the same swimming pool. If the two pumps are started together, at what time will the two pumps have emptied $$50$$% of the water in the swimming pool?


A
1 hour 12 minutes
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B
1 hour 20 minutes
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C
2 hour 30 minutes
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D
3 hours
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E
5 hours
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Solution

The correct option is D $$1\ hour\ 12\ minutes$$

Work efficiency of pump A in emptying pool = $$\dfrac{1}{4}$$ per hour

Work efficiency of pump B in emptying pool = $$\dfrac{1}{6}$$ per hour

$$\therefore$$ work done by A and B together = $$\dfrac{1}{4} + \dfrac{1}{6} = \dfrac{10}{24}$$per hour

Hence time taken to fill the tank  $$100$$% = $$\dfrac{24}{10}$$ hours

$$\therefore$$ time taken to fill $$50$$% = $$\dfrac{12\times 50}{5\times100}$$  = $$1.2$$ hours

Since, $$1 hour = 60 minutes$$

$$\therefore 1.2$$ hours= $$1.2\times 60 = 72$$ minutes

$$72$$ minutes = $$(60 +12)$$ minutes = $$1 hour$$  $$12 minutes$$

So, the answer is option A


Mathematics

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