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.**