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Alternate Working Days Completion Time

CAT 2021 Slot 2 · Quantitative Ability · Medium · Rates & Work

This is a medium Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests Rates & Work. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

  1. A.

    8

  2. B.

    6

  3. C.

    5

  4. D.

    7

Answer

D

Explanation

Let total work be LCM(15,12,20)=60\text{LCM}(15, 12, 20) = 60 units. Daily work rates:

  • Anu =6015=4= \frac{60}{15} = 4 units/day
  • Vinu =6012=5= \frac{60}{12} = 5 units/day
  • Manu =6020=3= \frac{60}{20} = 3 units/day

Work done on odd days (Vinu + Anu) =5+4=9= 5 + 4 = 9 units. Work done on even days (Vinu + Manu) =5+3=8= 5 + 3 = 8 units.

In a 2-day cycle, work done =9+8=17= 9 + 8 = 17 units. After 3 full cycles (6 days), work done =3×17=51= 3 \times 17 = 51 units. Remaining work =60−51=9= 60 - 51 = 9 units.

On the 7th day (odd day), Vinu + Anu work and produce 9 units, which completes the remaining work. Total days needed =6+1=7= 6 + 1 = 7 days.

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