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One worker or pipe joins or leaves partway: find the time

This type of question, asked 3 times: CDS 2 2016, CDS 2 2022, CDS 1 2023. All 4 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    CDS 2 2016

    37
    A tank can be filled by pipe XX in 2 hours and pipe YY in 6 hours. At 10 a.m. pipe XX was opened. At what time will the tank be filled if pipe YY is opened at 11 a.m. ?

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  2. Question 2

    CDS 2 2016

    17
    AA can do 50% more work than BB in the same time. BB alone can do a piece of work in 30 hours. BB starts working and had already worked for 12 hours when AA joins him. How many hours should BB and AA work together to complete the remaining work ?

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  3. Question 3

    CDS 2 2022

    13
    X and Y can do a piece of work in 45 days and 40 days respectively. They begin to work together, but X leaves after n days and then Y completes the remaining work in 23 days. What is n equal to ?

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  4. Question 4

    CDS 1 2023

    35
    Three taps A, B and C together can fill a tank in 6 hours. Tap C alone can fill the tank in 12 hours. To fill the tank, when it is empty, all the three taps are started together. After working t hours, tap C is closed and the tank is filled in 8 more hours. What is t equal to ?

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