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A worker leaves (or a pipe is closed) k days before completion: total time

This type of question, asked 4 times: 20 Jul 2023 S1, 27 Jul 2023 S2, 12 Sep 2024 S1, 19 Sep 2024 S3. All 4 questions below, oldest first.

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  1. Question 1

    20 Jul 2023 S1

    70
    A and B can individually complete a piece of work in 18 days and 30 days, respectively. A and B started working together, but A left 162316\frac{2}{3} days before the work is completed and B alone completed the rest of the work. For how many days did A work?

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  2. Question 2

    27 Jul 2023 S2

    68
    Benny can do a piece of work in 24 days. Chethan and David can do the same work individually in 36 and 48 days, respectively. All of them begin the work together. However, Benny leaves the work 4 days before the completion of work and Chethan leaves the work 10 days before the completion of the work. David worked till the end and completed the work. Find the number of days in which the work was completed.

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  3. Question 3

    12 Sep 2024 S1

    57
    Two pipes, A and B, can fill a tank in 10 minutes and 20 minutes, respectively. The pipe C can empty the tank in 30 minutes. All the three pipes are opened at a time in the beginning. However, pipe C is closed 2 minutes before the tank is filled. In what time, will the tank be full (in minutes)?

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  4. Question 4

    19 Sep 2024 S3

    51
    Two inlet pipes, P1 and P2, can fill a cistern in 20 hours and 30 hours, respectively. They were opened at the same time, but pipe P1 had to be closed 5 hours before the cistern was full. How many hours in total did it take for the two pipes to fill the cistern?

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