Question

A and B can do a piece of work in 10 days,B and C in 15 days and C and A in 12 days.In how many days can A, B and C finish it if they all work together? Also find the number of days B will require to finish the work if he works alone.

Answer 1

Given are the combination or pairing of persons to do a piece of work:

A+B = 10 days

B+C = 15 days

A+C = 12 days

Since there are 2 persons to accomplish the task, we multiply the number of days by 2.

A+B = 20 days

B+C = 30days

A+C = 24 days




Question: How long will B take to do it alone



From the given equations above, let

B = 20-A

B = 30-C

Since both equations are now equal to value of B,

20-A = -C

-A = 30-C-20

-A = 10-C

A = C-10

Substituting value of A on the third given equation:

(C-10)+C = 24

2C = 24 + 10

2C = 34

C = 17 days to complete the work alone

Using the second equation given above:

B + C = 30

B + 17 = 30-17 = 13



B = 13 days to complete the task alone

Using either the first or third equation above to get A:

A + B = 20 days

A + 13 = 20

A = 7 days to complete the work alone





The answer to the question is 13 days

Answer 2

Answer in Attachment.........