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 $= (\frac{1}{10} - \frac{1}{12}) = \frac{1}{60} . ∴ C a l o \neq c a n f \in i s h t h e w or k \in 60 d a y s .$

+ Report

Quizzes on Time & Work Ebook

Total Preview: 1089

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.