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One is k times as efficient and takes d days less than the other: time working together

The same question, asked 3 times: 14 Jul 2023 S2*, 21 Jul 2023 S1*, 21 Jul 2023 S2*. Every wording below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    14 Jul 2023 S2

    52
    P is two times more efficient than Q. P is able to complete a piece of work in 40 days less than Q. Working together, the whole number of days taken by them to complete the work is: (Round off to the nearest integer)

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  2. Question 2

    21 Jul 2023 S1

    68
    A works 3.5 times as fast as B, and A takes 45 days less than B to complete a job when each works alone. Calculate the number of days taken to complete the same job if A and B work together.

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  3. Question 3

    21 Jul 2023 S2

    61
    A works 5.4 times as fast as B, and A takes 22 days less than B to complete the job when each works alone. Calculate the number of days taken to complete the same job if A and B work together.

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