Level
2 Problems of time and work
Arun
and Aruna can complete a work individually in 12 working days and 15 working
days respectively with their full efficiencies. Arun does work only on Monday, Wednesday
and Friday while Aruna does the work on Tuesday, Thursday and Saturday. Sunday
is always off. But Arun and Aruna both work with half their efficiencies on
Friday and Saturday respectively. If Arun started the work in 1st
January which falls on Monday followed by Aruna on the next day and so on
(i.e., they work collectively in alternate days), then on which day work will
be completed?
Solution:
M T W Th F S
A Ar A Ar A Ar
Work 15%
+ 15% + 7.5%
= 37.5%
This pattern continued for
total 2 weeks only till 75% work got completed
Thus in 2 weeks they
will complete 75% work. Now 15% of the remaining (25% of the work) will be done
in the third week in Monday and Tuesday. Again 10% work remained undone. Out of
this 8.33% work will be done by Arun on Wednesday and remaining 1.66% work will
be completed on Thursday by Aruna
Final week
M T W Th F S
A Ar A Ar A Ar
Work 15%
+ 8.33%
+ 1.66%
= 25%
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