Question

a and b together can finish a piece of work in 3 days b and c together can finish it in 4 days and c alone can finish it in 6 days. how long will a alone take to finish the work?

Answer 1

a and b together will take 3 days to complete the work

b and c together will take 4 days to complete the work

c alone will take 6 days to complete the work

It can be written as

1/a + 1/b = 1/3 ----------------------------------------------(1)

1/b + 1/c = 1/4 ---------------------------------------------(2)

1/c = 1/6

Replace value of 1/c in equation (2)

1/b =1/4 - 1/6

So equation (1) becomes, 1/a + 1/4 - 1/6 = 1/3

1/a = 1/3 + 1/6 - 1/4

1/a =1/2 - 1/4

1/a = 1/4

So a alone takes 4 days to complete the work