CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and work. Another question on possible values. Conditions about men and women's efficiency is given and we need to find out the time taken by 'x' men and 'y' women. Finding one answer is usually far easier than finding "boundary conditions". But this boundary condition thing can be very instructive. CAT Questions from Time and Work.

Question 4: 4 men and 6 women complete a task in 24 days. If the women are at least half as efficient as the men, but not more efficient than the men, what is the range of the number of days for 6 women and 2 men to complete the same task?

1. 30 to 33.6 days
2. 32 to 35 days
3. 33.6 to 35 days
4. 30 to 35 days

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: Finding one answer is usually far easier than finding "boundary conditions". But this boundary condition thing can be very instructive.

4m and 6w finish in 24 days.
In one day, 4m + 6w = \\frac{1}{24}\\) of task.
In these questions, just substitute extreme values to get the whole range
If a woman is half as efficient as man
4m + 3m = \\frac{1}{24}\\), 7m = \\frac{1}{24}\\), m = \\frac{1}{168}\\)
6w + 2m = 3m + 2m = 5m, 5m will take \\frac{168}{5}\\) days = 33.6 days
If a woman is as efficient as a man
4m + 6w finish in 24 days
10m finish \\frac{1}{24}\\) of task in a day
6w + 2m = 8m, 8m will take \\frac{240}{8}\\) = 30 days to finish the task.
So, the range = 30 to 33.6 days. The new team will take 30 to 33.6 days to finish the task.

The question is "what is the range of the number of days for 6 women and 2 men to complete the same task?"

Hence, the answer is "30 to 33.6 days".

Choice A is the correct answer.