saswata4s
Twenty workers can finish a piece of work in 30 days. After how many days should 5 workers leave the job so that the work is completed in 35 days?
(A) 5 days
(B) 10 days
(C) 12 days
(D) 15 days
(E) 20 days
We are given that 20 workers can complete a job in 30 days. Since rate = work/time, the rate of the 20 workers is 1/30. We can let x be the number of days it would take 5 fewer workers (i.e., 15 workers) to complete the job (from beginning to end); thus the rate of the 15 workers would be 1/x. Let’s determine x using the following proportion:
20/(1/30) = (15)/(1/x)
600 = 15x
40 = x
Thus, the number of days it takes for the 15 workers to complete the job (from beginning to end) is 15 and their rate is 1/40.
However, we need to determine at what point in time 5 of the 20 workers should leave the job so that the work is completed in 35 days. We can let this be t, and note that the work done by the 20 workers in these t days plus the work done by the 15 workers after these t days (i.e., in 35 - t days) will be the complete job. Recall that work = rate x time, so we have:
(1/30)t + (1/40)(35 - t) = 1
t/30 + (35 - t)/40 = 1
Multiplying the equation by 120, we have:
4t + 3(35 - t) = 120
4t + 105 - 3t = 120
t + 105 = 120
t = 15
Answer: D