Question

Five men or ten women can complete a job in 20 days. In how many days can 3 men and 4 women complete it?
A. 10
B. 15
C. 20
D. 25

Answer 1

Hint: We will first find the amount of work done by 1 man and 1 woman in 1 day. After that, we will find the amount of work done by 3 men and 4 women in 1 day. And then we will divide the amount of work done from 1, which is the complete work to get the number of days.

Complete step by step answer:
In the question, we are given that 5 men or 10 women can complete a job in 20 days and we have to find the number of days in which the same amount of work can be completed by 3 men and 4 women. As per the question, we can say that,
5 men take 20 days to complete 1 work.
So, in 1 day, 5 men will complete $\dfrac{1}{20}$ part of the work.
So, in 1 day, 1 man can complete $\dfrac{1}{20\times 5}=\dfrac{1}{100}$ part of the work.
Let us now consider the work done by women. So, we have,
10 women take 20 days to complete 1 work.
So, in 1 day, 10 women will complete $\dfrac{1}{20}$ part of the work.
So, in 1 day, 1 woman can complete $\dfrac{1}{20\times 10}=\dfrac{1}{200}$ part of the work.
Now as we know that in 1 day, 1 man can complete $\dfrac{1}{100}$ part of the work, it means that,
In 1 day, 3 men can complete $\dfrac{1}{100}\times 3=\dfrac{3}{100}$ part of the work.
Similarly, we know that in 1 day 1 woman can complete $\dfrac{1}{200}$ part of the work, it means that,
In 1 day, 4 women can complete $\dfrac{1}{200}\times 4=\dfrac{4}{200}$ part of the work.
So, now we can find the total amount of work that can be completed by 3 men and 4 women in 1 day as,
$\begin{align}
  & \dfrac{3}{100}+\dfrac{4}{200} \\
 & \Rightarrow \dfrac{6+4}{200} \\
 & \Rightarrow \dfrac{10}{200}\Rightarrow \dfrac{1}{20} \\
\end{align}$
So, we can say that they can complete $\dfrac{1}{20}$ part of the work in 1 day.
Therefore, they can complete the whole work (1) in $\dfrac{1}{\dfrac{1}{20}}\times 1\Rightarrow 1\times 20\times 1\Rightarrow 20$ days.
Therefore, they will take 20 days to complete the work.
Hence, the correct answer is option C.

Note:
 Due to the confusion in the calculations in this question, the students should first find the amount of work done by 1 man in 1 day and by 1 woman in 1 day. And then find the amount of work done by the number of men and women asked for in the question, that is 3 and 4. The students should remember to take the complete work as 1 and consider it while calculating the number of days and amount of work. It is also advisable to step by step as there are chances of going wrong in this question, though it seems simple.