B is 20% more efficient than A. If B was 60% more efficient than A, then B…

2021

B is 20% more efficient than A. If B was 60% more efficient than A, then B could complete the work in 18 days lesser than number of days taken by A. What fraction of work would be left after 12 days, if A and B work together?

  1. A.

    1/5

  2. B.

    7/20

  3. C.

    11/20

  4. D.

    13/20

  5. E.

    9/20

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Show answer & explanation

Correct answer: E

Concept

Work problems compare workers by their per-day rate (efficiency). If one worker is k% more efficient than another, its rate is (1 + k/100) times the slower worker's rate, and the time taken is inversely proportional to the rate. The combined rate of two workers is the sum of their individual rates, the work finished in t days is (combined rate) x t, and the fraction left is 1 minus the fraction finished.

Application

  1. Let A take a days, so A's rate is 1/a of the work per day.

  2. In the hypothetical case B is 60% more efficient than A, so B's rate is 1.6/a and B's time is a/1.6 days.

  3. B is then faster than A by a - a/1.6 = 0.375a days, and this equals 18 days: 0.375a = 18, giving a = 48 days for A.

  4. Back to the real case: B is 20% more efficient than A, so B's time is 48/1.2 = 40 days. The rates are 1/48 (A) and 1/40 (B).

  5. Combined rate = 1/48 + 1/40 = 5/240 + 6/240 = 11/240 of the work per day.

  6. Work finished in 12 days = 12 x 11/240 = 11/20.

  7. Fraction left = 1 - 11/20 = 9/20.

Cross-check

Verify the hypothetical clue: with a = 48, B's hypothetical time is 48/1.6 = 30 days, and 48 - 30 = 18 days, exactly as given. So after 12 joint days the remaining work is 9/20.

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