Question

A and B together can complete a work in 10days. B and c together can complete it in 15 days. C and a together can do it in 12 days. how long will it take to them to finish the work if they work together

Answer 1

Answer:

Step-by-step explanation:

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