May 26, 2010

Question of the Day-Quantitative Ability

Question:
A contractor hired a group of men and women to do a piece of work in 12 days. But everyday for the first 12 days, one worker, either a man or a woman, was absent, and hence the work was delayed by 3 days. The contractor made an interesting observation that if the number of days for which women and men remained absent were interchanged, then the work would take 16 days to complete.

Approximately how many days would it take for one man and one woman to complete the work?

OPTIONS
1)16
2)20
3)24
4)Cannot be determined

Solution


Let there be a men and b women. Let initially men be absent for x days. Then women will remain absent for (12 – x) days.
Let us further assume that a man takes M days and a woman takes W days to complete the work when working alone. Then,




When men are absent on x days, and women on (12 – x) days, work is completed in 15 days.


 
 
When it is reversed, work is completed in 16 days.
 


 
 
Adding (ii) and (iii), we get,
 


 
 
 
 
 
 
Substituting from (i), we have
 
 


 
 
 
 
 
 
 
 
 
Hence, option 2.



 
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