Question

A can do a piece of work in x days and B can do the same work in (x+16) days. If both working together can do it in 15 days, find the number of days in which each of them can do
the work separately.​

Answer 1

Answer:

Step-by-step explanation:

1/A + 1/B = 1/12

1/B + 1/C = 1/15

1/C + 1/A = 1/20

Hence, 2(1/A + 1/B + 1/C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5

Therefore 1/A + 1/B + 1/C = 1/10

Now, 1/B + 1/C = 1/15

Therefore 1/A = 1/10 - 1/15 = 1/30.

Similarly, 1/B = 1/10 - 1/20 = 1/20, and 1/C = 1/10 - 1/12 = 1/60.

Thus it will take 30 days for A, 20 days for B and 60 days for C to complete the same work separately.