Question

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?

Answer 1

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.

Complete step by step answer:
According to the given question we can see that some tasks are given to women and men and we need to find the time taken by both of them to do the task together. Also, in the question we are provided with the information that how much time is taken by women alone in order to complete the work and similarly for men it is given.
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.

Note: In the given question or we can say in the word problems our main mistake is that we don’t study the statement properly and just start solving which leads to errors. Also, while solving word problems first we need to find the value of whatever concept is involved in units and then we should proceed further.