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Work and Time Allocation

XAT 2018 · Quantitative Ability & Data Interpretation · Medium · Quantitative Aptitude

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Abdul, Bimal, Charlie and Dilbar can finish a task in 10, 12, 15 and 18 days respectively. They can either choose to work or remain absent on a particular day. If 50 percent of the total work gets completed after 3 days, then, which of the following options is possible?

  1. A.

    Each of them worked for exactly 2 days.

  2. B.

    Bimal and Dilbar worked for 1 day each, Charlie worked for 2 days and Abdul worked for all 3 days.

  3. C.

    Abdul and Charlie worked for 2 days each, Dilbar worked for 1 day and Bimal worked for all 3 days.

  4. D.

    Abdul and Dilbar worked for 2 days each, Charlie worked for 1 day and Bimal worked for all 3 days.

  5. E.

    Abdul and Charlie worked for 1 day each, Bimal worked for 2 days and Dilbar worked for all 3 days.

Answer

E

Explanation

Let total work = LCM(10, 12, 15, 18) = 180 units.

Work done per day:

  • Abdul: 180/10=18180 / 10 = 18 units
  • Bimal: 180/12=15180 / 12 = 15 units
  • Charlie: 180/15=12180 / 15 = 12 units
  • Dilbar: 180/18=10180 / 18 = 10 units

50% of the total work = 90 units.

Testing option E:

  • Abdul (1 day) + Charlie (1 day): 1imes(18+12)=301 imes (18 + 12) = 30 units
  • Bimal (2 days): 2imes15=302 imes 15 = 30 units
  • Dilbar (3 days): 3imes10=303 imes 10 = 30 units Total = 30+30+30=9030 + 30 + 30 = 90 units.

Hence, Option E is possible.

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