Work and Time - Quant/Math - CAT 2010
Question 4 the day:
June 6, 2002
The question for the day is from the topic work and time.
- Four men and three women can do a job in 6 days. When five men and six women work on the same job, the work gets completed in 4 days. How long will a woman take to do the job, if she works alone on it?
| (1) | 18 days | | (2) | 36 days | | (3) | 54 days | | (4) | None of these |
Correct Answer - (3)
Solution:
Let the amount of work done by a man in a day be ‘m’ and the amount of work done by a woman in a day be ‘w’.
Therefore, 4 men and 3 women will do 4m + 3w amount of work in a day. If 4 men and 3 women complete the entire work in 6 days, they will complete 1/6th of the work in a day.
Hence eqn (1) will be 4m + 3w = 
and from statement (2), eqn (2) will be 5m + 6w = 
Solving eqn (1) and eqn (2), we get 3m =  or m = 1/36. i.e. a man does 1/36th of the work in a day. Hence he will take 36 days to do the work.
Substituting the value of m in eqn (1), we get 
=> 3w =  or w = 1/54. i.e. a woman does 1/54th of the work in a day. Hence she will take 54 days to do the entire work.
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