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# Ten women can complete a piece of work in 15days. Six men can complete a piece of work in 10 days. In how many days can 5 women and 6 men together complete the piece of work?

Last updated date: 13th Jul 2024
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Hint: According to the given question it is clear that it is word problem type question. Also, from the question we can say that it involves the concept of work and time and then we need to evaluate the time taken by women and men to complete the given task together at the same.

One woman can complete work in one day is $=\dfrac{1}{15\times 10}=\dfrac{1}{150}$
One man can complete work in one day is $=\dfrac{1}{6\times 10}=\dfrac{1}{60}$
Therefore, work completed by 5 women and 6 men is $\dfrac{5}{150}+\dfrac{6}{60}$
Now, simplifying the above term we get $\dfrac{1}{30}+\dfrac{1}{10}$
Now, taking the lcm and adding we get, $\dfrac{4}{30}$ which is equivalent to $\dfrac{2}{15}$ .
Therefore, 5 women and 6 men can complete the work in $\dfrac{15}{2}$ that is 7.5 days.