20 archivists can catalog a collection in 15 days. After how many days

Question

20 archivists, each working at the same constant rate, can catalog a collection in 15 hours. After how many hours from the start should 8 archivists be reassigned and stop working so that the remaining archivists finish cataloging the entire collection in 10 hours after the reassignment?

A. 6
B. 7
C. 8
D. 9
E. 10

A. 6
B. 7
C. 8
D. 9
E. 10

M47-05

Bunuel · Accepted Answer

GMAT Club Official Solution:

Total work = 20*15 = 300 units.

After reassignment, remaining archivists = 20 - 8 = 12.

They finish in 10 more hours, so remaining work at reassignment = 12*10 = 120 units.

Work completed before reassignment = 300 - 120 = 180 units.

Rate before reassignment = 20 per hour.

Hours before reassignment = 180/20 = 9.

Answer: D.

Dereno · Answer

Let the rate of archivists be a.

Total work = 20*15*a = 300a

After 8 archivists leave, we are left with 12 archivists.

Total work = 12 * 10*a = 120a

Remaining work = 300a - 120a = 180a

Let d be the number of days, all archivists worked together before 8 of them left.

180a = 20 * d * a

Thus,  d = 9

Option D

S9564 · Answer

Bunuel : Could you pls explain this solution. not getting it.

vasu1104 · Answer

rate of 20 people = x/15 
now these 20 people work for some t hrs.

so work done = xt/15

after than 8 are removed and only 12 are working for 10 hrs to finish the job.

we know rate of 1 person = x/300
so for 12 people rate= 12x/300 = x/25

these people work for 10 hrs.
so work done= 10x/25 = 2x/5

so,
xt/15 + 2x/5 = x
t =9 hrs

choice D

kevincan · Answer

The remaining archivists constitute 3/5 of the total , and they will be working for 2/3 of the 15 hours. They will do 2/5 of the total job, so the other 3/5 must be done before the reassignment, and 3/5 of 15 hours is 9 hours.

joshuadlima1 · Answer

The rate of 12 analysts is 12/20 * (1/15) = 1/25.

1/15 * H + 1/25 * 10 = 1 (Total Complete)

1- 1/25 * 10 = 15/25 = 3/5 or 9/15.

1/15 * H = 9/15

H = 9 hours.

Hope it's clear.

sunshineeee · Answer

Total work = D = R * T

D=20*15=300 units

D after the reassignment -> 
archivist work: 20-8=12
So, D = 12*10=120 units

D before the reassignment -> 300-120=180 units

Question: T before reassignment
T=D/R = 180/20 =  9H (Answer D)

20 archivists can catalog a collection in 15 days. After how many days

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GMAT Problem Solving (PS) Questions

20 archivists can catalog a collection in 15 days. After how many days

Prep Toolkit

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