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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

Question

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

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Solution

To solve this problem, we first need to find out the work done by Anu, Vinu, and Manu in one day.

  1. Anu's one day work = 1/15
  2. Vinu's one day work = 1/12
  3. Manu's one day work = 1/20

Next, we need to find out the work done by all three in two days, as Anu and Manu are working on alternate days.

Work done in two days = 2*(Vinu's one day work) + Anu's one day work + Manu's one day work = 2*(1/12) + 1/15 + 1/20 = 1/6 + 1/15 + 1/20 = 15/60 + 4/60 + 3/60 = 22/60 = 11/30

So, they complete 11/30 of the work in 2 days.

To find out the number of days they will take to complete the work, we divide 1 (the whole work) by the work done in two days and multiply by 2.

Number of days = (1 / (11/30)) * 2 = 30/11 * 2 = 60/11

Since we can't have a fraction of a day, we round this up to the nearest whole number, which is 6.

So, they will take approximately 6 days to complete the work.

This problem has been solved

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