Question

A can complete a piece of work in 36 days, B in 40 days and C in 60 days. B and C
together start the work and leave the work after 4 days. Find the time taken by A to
complete the remaining work ?​

Answer 1

Answer:

If A and B together can do a work in 36 days, B and C in 60 days, and A and C in 45 days, in how many days can A alone do the this work? The options are 180, 100, 90, and 60.

If A and B together can do a work in 36 days, B and C in 60 days, and A and C in 45 days in how many days can A alone do the work? The options are 180, 100, 90, and 60.

A and B do 1/36th of the work in a day.

B and C do 1/60th of the work in a day.

A and C do 1/45th of the work in a day.

Now for LCM of 36, 60 and 45

36 = 2x2x3x3

60 = 2x2x3x5

45 = 3x3x5

SO LCM = 2^2x3^2x5 = 180

Thus 2A, 2B and 2C can do (1/36)+(1/60)+(1/45) = (5/180) + (3/180) + (4/180) = 12/180 = 1/15

So A, B and C do 1/30 of the work in a day.

So A alone does (1/30) -(1/60) = (2/60)-(1/60) = 1/60th part of the work in a day.

So A working alone can complete the work in 60 days.