A can do a piece of work in 57 hours, B and C together can do it in 28 hours, while A and C together can do it in 19 hours. How long (in hours) will B alone take to do it?​

Correct option is C

Given:

Time taken by A to complete the work = 57 hours

Time taken by B and C together to complete the work = 28 hours

Time taken by A and C together to complete the work = 19 hours

Objective: Find the time taken by B alone to complete the work

Formula Used: ​

Total work = work rate $$\times$$ time​

Solution:

Total work = LCM(57, 28, 19) = 1596 units

A’s rate = $$\frac{1596}{57}$$​ = 28 units/hour

B and C’s combined rate = $$\frac{1596}{28}$$​ = 57 units/hour

A and C’s combined rate = $$\frac{1596}{19} = 84 \, \text{units/hour}$$​​

C's work rate = 84 - 28 = 56 unit/hour

B's work rate = 57 - 56 = 1 unit/hour

Time taken by B alone =  $$\frac{1596}{1} = 1596 \, \text{hours}$$​​