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.

a. 144 days

Answer 1

a+b+c=72

c=2ab

b=4ac

since a and b completes twice work when working together compared to c working alone  why  divide 72 by 2=72/2=36

similarly a and c completes four  times a work work when working together compared to  working alone  why  divide 72 by 4=72/4=18

add all the three

72+36+18=126 days

Answer 2

a, b and c can do the work in 72 days:

⇒ a + b + c = 72 days

a and b together can do two times as much work as c alone

⇒ a + b = 2c

Replace (a + b) = 2c into  a + b + c = 72 days

2c + c = 72

3c = 72

c = 72 x 3 = 216 days

⇒ c can do the work in 216 days alone.

Answer: c can do the work in 216 days alone