A, B and C can do a piece of work in 11 days, 20 days, 20 days and 55

Question

A, B and C can do a piece of work in 11 days, 20 days, and 55 days, respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?

(A) 7 days 
(B) 8 days
(C) 9 days 
(D) 10 days
(E) 11 days

waytowharton · Answer

Let's assume work to be 220 units. Work done by A,B,C per day is 20,11 and 4 respectively. Since B and C work on alternate days. Hence work done in 2 days = 2*A+B+C = 55. Total work to be done in 220. Hence we need 4 cycles of 2 days. Hence 8.

abhimanyujain1711 · Answer

hi bunuel,

i have a question.

total task is 220 units. 
speeds 
A=20
B=11
C=4 all speeds in units per day.

_ _ _ _ _ _ _ = 7 days

the above dashs are the days.

A= 20*7 = 140
B and C assist on 1st,3rd,5th and 7th day. 
so basically - 15*4 = 60 units

140 + 60 = 220 units

the task finishes in 7 days.

please advice

Sahil20o7 · Answer

a works with b on day 1 and a works with c on day 2 and so on.

CrackverbalGMAT · Answer

A, B and C can do a piece of work in 11 days, 20 and 55 days, respectively, working alone. How soon can the work be done if A is assisted by B and C on alternate days?

Let' s use LCM method is solve this work related problem.

Assume that total work = LCM (11,20,55) = 220 units

Calculating the per day work:

Amount of work done by A in one day = 220/11 = 20 units
Similarly , B in one day = 220/20 = 11 units
C in one day = 220/55 = 4 units

How soon can the work be done if A is assisted by B and C on alternate days?

A will be working everyday and (B and C ) will join A on every alternate days i.e 2 nd day, fourth day...
Per day work of A = 20 units
Per day work of B and C = 11 + 4 = 15 units

First day : A will complete 20 units
Second day: A,B and C together will complete 20+11+4 = 35 units

That means (20 + 35) = 55 units are completed in every 2 days.

Total work to complete = 220 units

Since 55 units are completed in 2 days , (55* 4) = 220 units will be completed in 2*4 = 8 days

Option B is the answer.

Thanks,
  Clifin J Francis,
GMAT SME

Surgicalgoblin · Answer

Assume that total work = LCM (11,20,55) = 220 units

Calculating the per day work:

work done by A in one day = 220/11 = 20 units
B in one day = 220/20 = 11 units
C in one day = 220/55 = 4 units

If we assume that A worked for x days and b and c worked for half that amount then the equations comes out to be 
20x + 15x/2 = 220.
solving we get x= 8.

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A, B and C can do a piece of work in 11 days, 20 days, 20 days and 55

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