a and b can do a piece of work in 12 days, Time & Work, General Mathematics

Question:A and B can do a piece of work in 12 days ; B and C can do it in 15 days ; A and C  can do it in 20 days. In how many days will A, B and C finish it, working all together ?

Also, find the number of days taken by each to finish it working alone.

Answer (A + B)'s 1 day's work` = 1/12;` (B + C)' s 1 day's work` = 1/15`

and (A + C)'s 1 day's work` = 1/20`

Adding, we get : 2 (A + B + C)'s 1 day's work

`= (1/12 + 1/15 + 1/20) = 1/5.`

:. (A + B + C)' s 1 day's work` = 1/10`

Thus A,B and C together can finish the work in 10 days.

Now A's 1 day's work

 = [(A + B + C)'s 1 day's work] - [(B + C) 's 1 day's work] 

`= (1/10 - 1/15) = 1/30`

A alone can finish the work in 30 days.

Similarly, B's 1 day's work` = (1/10 - 1/20) = 1/20`

:. B alone can finish the work in 20 days.

And C's 1 day's work` = (1/10 - 1/12) = 1/60.

:. C alone can finish the work in 60 days.

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A and B can do a piece of work in 12 days ; B and C can do it in 15 days ; A and C can do it in 20 days. In how many days will A, B and C finish it, working all together ? Also, find the number of days taken by each to finish it working alone.

Question:A and B can do a piece of work in 12 days ; B and C can do it in 15 days ; A and C can do it in 20 days. In how many days will A, B and C finish it, working all together ? Also, find the number of days taken by each to finish it working alone.