Question

A,B and C can together do some work in 72 days. A and B together do two times as much work as C alone, and A and C together can do our times as much word as B alone. Find the time taken by C alone to do the whole work.

Answer 1

the work done by A, B and C together

A + B + C =>72 days  ------(1)

A + B =2C    ---------(2)

A + C = 4B -----------(3)

subtitute (2) in (1) we get

2C + C => 72 means that three C can do that work in 72 days

so one C take 72 x 3 days ie. 216 days

Answer 2

Time taken by A ,B and C  together to finish a work = 72 days

Let time taken by A alone to finish the work = x days

time taken by B alone to finish the work = y days

time taken by C alone to finish the work = z days

→ The equation of one days work is given by

 1/x + 1/y+1/z  = 1/72..............(A)

Also,A and B together can do two times as much work as C alone, and A and C together can do four times as much word as B alone

→ 1/x + 1/y = 2/ z  .......(1)

→ 1/x +1/ z = 4/ y  

Substituting (1) in A, we get

→2/z+1/z=1/72

→3/z=1/72

→ z=3×72=216 days

Time taken by C alone to do the whole work = 216 days