3 small pumps and a large pump are filling a tank. Each of the three small pumps works at 2/3rd the rate of the large pump. If all 4 pumps work together, they should fill the tank in what fraction of the time that would have taken the large pump alone?

Correct Answer: 1/3rd of the time

Rate of filling by each small pump = 2/3rd of that of large pump.

Therefore, rate of filling by 3 small pumps = 3×2/3 of that of large pump = twice of that of large pumps.

If all 4 pumps work together, they will fill as much water as that by 3 large pumps.

Therefore, time taken by 4 pumps = 1/3 of the time taken by large pump.