EduGoog

Time & Work

A report of 100 pages is to be typed by three typists.
Typist A can type 100 pages in 10 hours.
Typist B can type the same pages in 20 hours. and 
Typist C can type in 25 hours,
All the three typist started typing at 09:00 A.M. At 01:00 P.M., Typist A stopped typing. The other two typist finished the job Approximately at what time the report was typed ?

Option:
A. 04:00 p.m.
B. 03:40 p.m.
C. 04:40 p.m.
D. None of these
Answer: B . 03:40 p.m.

Justification:

A's 1 hours work = 100 / 10 = 10 pages.
B's 1 hours work = 100 / 20 = 5 pages. 
C's 1 hours work = 100 / 25 = 4 pages.
(A + B + C)'s 1 hour work = (10 + 5 + 4)pgs. = 19 pages.
Since the work started at 9:00 a.m.
Work done by A, B and C from 9:00 a.m. to 1:00 p.m. 
i.e. 4 hours = 19 x 4 pages = 76 pages.
Balance work = (100 -  76)pages = 24 pages.
This work was done by B and C from 1:00 p.m. onwards.
(B + C)'s 1 hour work = (5 + 4) pages = 9 pages.
For typing 24 pages, time required by B + C = 1/9 x 24 = 2.40 hours (approx.)
Hence, the work was completed at 1:00 + 2:40 i.e., 3:40 p.m. 

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