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10 Mar 2026, 11:44
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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
10 Mar 2026, 11:44
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Official Solution:
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
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
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
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
