Question

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 

Answer 1

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.