Question

a and b can do a piece of work in 6 days, b and c together in 10 days, c and a together in 7.5 days. in how many days can a, b and c individually completes the work?

Answer 1

Given that A and b can do a piece of work in 6 days,

b and c together in 10 days,

c and a together in 7.5 days.

In other words, A&B can do 1/6 of work in one day

B&C can do 1/10 of work in one day

C&A can do 1/7.5 of work in one day

Adding these we have

Twice (A,B,C) together can do in one day = $\frac{1}{6} +\frac{1}{10} +\frac{1}{7.5} =\frac{24}{60}$

Hence A,B,C together can do 12/60 of full work in one day.

So A,B,C together can complete in 5 days.

1/5 -1/10 = 1/10.  Hence A alone can complete in 10 days

1/5-1/7.5 = 1/15  Hence B alone can complete in 15 days

1/5 -1/6 =1/30: Hence C alone can complete in 30 days.