Working 8 hours a day, workers were scheduled to construct a

Question

Working 8 hours a day, workers were scheduled to construct a new wing of Holy Grace Hospital in 180 days. After one-third of the work had been completed according to schedule , 20 workers quit and were not replaced. As a result, construction took a total of 300 days to complete, even though each remaining worker worked 9 hours a day. Assuming that all workers are equally productive and that their productivity does not vary from hour to hour, how many workers were initially assigned to the project?

(A) 27
(B) 36
(C) 40
(D) 45
(E) 48

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Official Answer

B

(A) 27
(B) 36
(C) 40
(D) 45
(E) 48

HarshavardhanR · Answer

Let n be the initial number of workers assigned to the project.
Let R be the rate of work of a worker i.e., amount of work done by a worker in an hour.

The work W is nothing but the output of n workers, working 8 hours a day, for 180 days, each with an output of R per worker per hour.

i.e.,

Work = (n) (8) (180) (R)

Work done as per schedule = 1/3 (work) = (n) (8)  (60)  (R)

Rest of the work = 2/3 (Work) = (n) (8)  (120)  (R)

This remainder work is done by (n-20) workers, working 9 hours a day in (300 - 60 = 240) days.

i.e.,

(n - 20) (9) (240) (R) = (n) (8) (120) (R)

=> n/(n-20) = 9/4

=>   n = 36. Choice B  .

---
Harsha

kevincan · Answer

Also , the remaining two thirds should have completed in the following 120 days , but in reality , 240 days (twice as many days) were needed , even though the each of the remaining workers was 9/8 as productive as before (in terms of work per day). Thus the remaining workers in total did 1/2 * 8/9 = 4/9 as much work per hour as the initial workers did before , so the 20 workers who quit must have constituted 5/9 of the initial workforce. Therefore , the initial workforce must have been composed of 20(9/5) =36 workers

SHASHAM · Answer

let initial workforce be x 
then the amount of time they take to finish complete work is 180*8 - 1440 hours 
their rate is 1/1440 
therefore to finish 1/3rd work they will take 480 hours which is 60 days 
so the remaining 2/3rd work was supposed to be completed in 180-6 = 120 days

and for x-20 work force since they complete the work in 300 days the initial 60 days needs to be substarcted as the remaining 2/3rd work will be done in 240 days now at 9 hours per day
so thats 240 *9

now equating the worker days hours x*120*8 = (x-20)*240*9
when you solve for x answer is 36

option b

Working 8 hours a day, workers were scheduled to construct a

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