A cistern can be filled by two pipes P & Q in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?

Question: A cistern can be filled by two pipes P & Q in 20 and 30 min respectively. Both pipes being open, when must the first pipe be turned off so that the cistern may be filled in 10 minutes more?

Solution:
In 1 min both pipes can fill = (1/20) + (1/30)
= (3 + 2)/60
= 5/60 = 1/12
In 10 min second pipe can fill = (1/30) × 10 = 1/3 part

Part of cistern filled by both the pipes = 1 - 1/3
= (3 - 1)/3 = 2/3

1/12 part is filled in 1 min
∴ 2/3 part will be filled in (12 × 2)/3 = 8 min
Hence, the first pipe should be turned off after 8 min.