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    Question

    A team of workers can finish a task in 36 days. However, 5

    workers leave the task every day, and it gets done in 48 days. Find the time needed for 90 workers to complete the task working together.
    A 125 Correct Answer Incorrect Answer
    B 188 Correct Answer Incorrect Answer
    C 225 Correct Answer Incorrect Answer
    D 195 Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    ATQ,

    Let the number of workers be 'W' and each has efficiency 'e' units/day.

    Total work = W × 36 × e = 36We units.

    ATQ:

    36We = W × e + (W - 5 × 1) × e + (W - 5 × 2) × e + .... + (W - 5 × 47) × e

    Or,

    36W = 48W - 5 × (1 + 2 + 3 + .... + 47)

    ⇒ 12W = 5 × 47 × (48/2)

    ⇒ W = (5 × 47 × 24) ÷ 12 = 470

    Let the required time be T days for 90 workers.

    So, 36 × 470 × e = 90 × T × e

    ⇒ T = (36 × 470) ÷ 90 = 188

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