Question

A and b can do a piece of work in 72 days .b and c can do it in 120/days.a and c can do it in 90 days.in what time can a alone do it

Answer 1

a and b together take 72 days to complete the work

b and c together take 120 days to complete the work

a and c together take 90 days to complete the work

It can be written as

1/a + 1/b = 1/72

1/b + 1/c = 1/120 ----------------------------------------------(1)

1/a + 1/c = 1/90

Sum of above three equations will be

2/a + 2/b + 2/ c= 1/72 + 1/120 + 1/90

L.C.M of 72, 120 and 90 = 360

2(1/a + 1/b + 1/c) = (5+4+3)/360 = 1/30

(1/a + 1/b + 1/c) = 1/60 --------------------------------------------- (2)

So, work completed by a, b and c together = 60 days

Now equation (2) – (1) gives the work done by a alone

1/60 – 1/120 = 1/60 x (1-(1/2)) = 1/120

So, it takes 120 days for a alone to complete the work