Question

In how many days can 10 women finish a work? 10 men can complete the work in 6days. 10 men and 10 women can together complete the work in $3\dfrac{3}{7}$ days. If 10 men work for three days and thereafter 10 women replace them, the remaining work is complete in 4 days.

Answer 1

Hint: In the given question, we are given various situations of work done. Men and women were given some work, so for the same we are given various situations like time taken by 10 men to complete work is 6 days and if 10 men and women work together then it is $3\dfrac{3}{7}$days and further after defining number of men and women we are given situation and are asked to find the time taken by 10 women.

Complete step-by-step solution:
According to the question, we need to find the work done by 10 women and time taken by men and women and men alone to do the same work is given.
Now, work done by 10 women in one day is $\dfrac{7}{24}-\dfrac{1}{6}=\dfrac{1}{8}$
Therefore, 10 women can complete the work in 8 days.
Now, by using second and third condition, let 10 men can finish work in x days and 10 women can finish work in y days then $\Rightarrow \dfrac{1}{x}+\dfrac{1}{y}=\dfrac{7}{24}$ and from second and third condition, $\dfrac{3}{x}+\dfrac{4}{y}=1$ and we know x is 6 days.
Therefore,
$\begin{align}
  & \dfrac{4}{y}=\dfrac{1}{2} \\
 & \Rightarrow y=8 \\
\end{align}$
Hence, the time taken by 10 women to complete the work is 8 days.

Note: In such questions, we need to be aware of the concept of work done and need to find the value in one unit for every man and woman and the one-day task in order to correctly interpret the question and get the correct answer.