# Two taps fill a cistem at the rate of 1 litre per minute and 2 litres per minute, respectively. A third tap empties it at rate of $\frac{1}{2}$ litr

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Two taps fill a cistem at the rate of 1 litre per minute and 2 litres per minute, respectively. A third tap empties it at rate of $\frac{1}{2}$ litre per minute. If the capacity of the cistem is 1000 litres, then how much time will it take to fill it if all the three taps are open ?

1. 7 hrs
2. 6 hrs 40 min
3. 6 hrs 30 min
4. 6 hrs

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Correct Answer - Option 2 : 6 hrs 40 min

Given :

Two taps fill a cistem at the rate of 1 litre per minute and 2 litres per minute, respectively and a third tap empties it at rate of $\frac{1}{2}$ litre per minute.

Concept used :

Total time = Total work/Work per unit time

Calculations :

Total fiiling capacity of all pipes = 1 + 2 - (1/2)

⇒ 3 - 0.5

⇒ 2.5 litres/min

Total times to fill the 1000 litres cistern = 1000/2.5

⇒ 400 minutes or 400/60 hours

⇒ 6 hours 40 minutes

∴ Option 2 will be the correct answer.