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Answer»

Solution

Let the amount of work done by a woman in a day be W and let the amount of work done by a man in a day be M.
We need to find the value of W to be able to find the number of days it TAKES 10 women to FINISH the work.

Statement 1 implies that: $5M = \frac{1}{8}$
So, $M=\frac{1}{40}$

Statement 2 implies that: $6M+4W = \frac{1}{5}$

Statement 3 implies that $M+W = 3W => M=2W$

Clearly using just one statement, we can't find the value of W. But using any PAIR of statements, we can find the value of W as shown below.

Using Statement 1 and 2: $M=\frac{1}{40}$ and $6M+4W = \frac{1}{5}$
So, $\frac{6}{40}+4W=\frac{1}{5}$
So, $4W =\frac{1}{20}$ or $W=\frac{1}{80}$
So, 1 woman can do the work in 80 days and 10 women can do the work in 8 days.

Using Statement 1 and 3: $M=\frac{1}{40}$ and $M=2W$
So, $2W=\frac{1}{40}$ or $W=\frac{1}{80}$
So, 1 woman can do the work in 80 days and 10 women can do the work in 8 days.

Using Statement 2 and 3: $M=2W$ and $6M+4W = \frac{1}{5}$
So, $12W+4W = \frac{1}{5}$ or $16W=\frac{1}{5}$
So, $W=\frac{1}{80}$
So, 1 woman can do the work in 80 days and 10 women can do the work in 8 days.

As can be seen above, the question can be answered using any two statements of the three.



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