Question

pipes A&B can separately fill a tank in 75minutes and 90 minutes respectively.pipe C can empty the tank in 3hr. All the three pipes are opened simultaneously. After half an hour, pipes A & B are stopped while C continues it's work. How long will pipe C can take now to empty the tank?​

Answer 1

Pipe C will empty the tank in 102 minutes.

Step-by-step explanation:

Pipes A and B fill the tank in 75 minutes(1.25 hours) and (1.50 hours) respectively.

Therefore, fraction of tank filled by both the pipes in one hour = $\frac{1}{1.25}+\frac{1}{1.5}=\frac{1.5+1.25}{1.875}$

= $\frac{2.75}{1.875}$

Fraction of tank filled in 0.5 hours = $\frac{2.75}{3.75}$

= $\frac{11}{15}$

Since pipe C empties the tank in 3 hours then fraction of tank emptied in 1 hour = $\frac{1}{3}$

Fraction of tank emptied in 0.5 hours = $\frac{1}{6}$ hours

Remaining part of the tank after 0.5 hour = $\frac{11}{15}-\frac{1}{6}=\frac{22-5}{30}$

= $\frac{17}{30}$

Remaining portion of the water tank will be emptied by the pipe C = $\frac{\frac{17}{30}}{\frac{1}{3}}$

= $\frac{17}{10}$

= 1.7 hours

≈ 102 minutes

Therefore, Pipe C will take 102 minutes to empty the tank.

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