Question

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?
30 to 33.6 days
32 to 35 days
33.6 to 35 days
30 to 35 days

Answer 1

23.....................

Answer 2

The range of the number of days for 6 women and 2 men to complete the same task is 30 to 33.6 days

Solution:

Let "m" represent men

Let "w" represent women

4 men and 6 women complete a task in 24 days

Therefore,

$In\ one\ day\ 4m + 6w = \frac{1}{24}\ of\ work$

If a woman is half as efficient as man, then

2w = 1m

6w = 3m

Therefore,

$4m + 3m = \frac{1}{24}\\\\7m = \frac{1}{24}\\\\m = \frac{1}{168}$

Number of days for 6 women and 2 men to complete the same task is:

6w + 2m = 3m + 2m = 5m

$5m = \frac{5}{168}$

Thus, they will take : $\frac{168}{5}\ days = 33.6\ days$

Given that,

4m + 6w finish in 24 days

Thus,

4m + 6m finish in 24 days

$10m\ finish\ \frac{1}{24}\ of\ work\ in\ a\ day$

Therefore,

1m finish in $\frac{1}{240}$ of work in a day

6w + 2m = 8m

8m will take 240/8 = 30 days to finish the work

So, the range is 30 to 33.6 days

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