Pipe & Work Question Answers

Work and Time - Quant/Math - CAT 2008

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)

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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 = 1/6   
and from statement (2), eqn (2) will be 5m + 6w = 1/4

Solving eqn (1) and eqn (2), we get 3m =1/12 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 4 * 1/36  +  3w  =  1/6

=> 3w =1/6-1/9  = 3-2 / 18 = 1/18   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.