a and b can do a piece of work in 10 days, b and c in 15 days, c and a in 18 days. in how many days can b alone do it
Answers
Given are the combination or pairing of persons to do a piece of work:
A+B = 10 days
B+C = 12 days
A+C = 15 days
Since there are 2 persons to accomplish the task, we multiply the number of days by 2.
A+B = 20 days
B+C = 24 days
A+C = 30 days
Question: How long will B take to do it alone
From the given equations above, let
B = 20-A
B = 24-C
Since both equations are now equal to value of B,
20-A = 24-C
-A = 24-C-20
-A = 4-C
A = C-4
Substituting value of A on the third given equation:
(C-4)+C = 30
2C = 30 + 4
2C = 34
C = 17 days to complete the work alone
Using the second equation given above:
B + C = 24
B + 17 = 24
B = 7 days to complete the task alone
Using either the first or third equation above to get A:
A + B = 20 days
A + 7 = 20
A = 13 days to complete the work alone
The answer to the question is 7 days