A tank can be filled by pipe P in 2 hours and pipe Q in 6 hours. At 10 am pipe P was opened. At what time will the tank be filled if pipe Q is opened at 11 am?

Question

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish the job. However, they all worked together for 6 days, followed by Rakshita, who worked alone for 3 more days to finish the job. If Rakshita had worked alone on the job then the number of days she would have taken to finish the job, cannot be

Answer 1

Step 1: Find the rates.
Pipe P fills the tank in 2 hours, so in one hour it fills $\frac{1}{2}$ of it. Pipe Q fills it in 6 hours, so in one hour it fills $\frac{1}{6}$.

Step 2: Work done by P alone.
P opens at 10 am and Q opens at 11 am. So P works alone for 1 hour and fills $\frac{1}{2}$ of the tank.

Step 3: What is left.
Half the tank is filled, so $\frac{1}{2}$ is still empty after 11 am.

Step 4: Combined rate.
From 11 am both work together. Their joint rate is \[ \frac{1}{2} + \frac{1}{6} = \frac{3}{6} + \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \] tank per hour.

Step 5: Time for the rest.
Time needed is the remaining work divided by the joint rate, $\frac{1/2}{2/3} = \frac{3}{4}$ hour, which is 45 minutes.

Step 6: Final time.
Add 45 minutes to 11 am to get 11:45 am.
Answer: 11:45 AM

A tank can be filled by pipe P in 2 hours and pipe Q in 6 hours. At 10 am pipe P was opened. At what time will the tank be filled if pipe Q is opened at 11 am?

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The Correct Option is C

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