Question

If one man or two women or three boys can do a piece of work in 22 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in:
A. 8 days
B. 12 days
C. 6 days
D. 11 days

Answer 1

Hint: For solving this question you should know about calculating efficiency for a unit. In this question we will determine the work done by 1 man in one day and this can be determined by finding the efficiency and same way we have to determine the work done by 2 women in one day, which can be determined by finding the efficiency. And the same as determining the work done by 3 boys in one day which can be determined by finding the efficiency. Now we have to determine the efficiency of all the people which can be determined by finding the sum of all the work done in one day.

Complete step-by-step solution:
According to the question if one man, one woman and one boy do the same work in how many days, then: First of all we have to assume that the same piece of work will be done by 1 man or 1 woman or 1 boy in x days as mentioned in the solution hint. Now, we have to determine the work done by 1 man in one day which can be determined by finding the efficiency as below,
$=\dfrac{x}{22}\ldots \ldots \ldots \left( i \right)$
Now, we have to determine the work done by 2 women in one day which can be determined by finding the efficiency as below,
$=\dfrac{x}{2\times 22}\ldots \ldots \ldots \left( ii \right)$
Now, we have to determine the work done by 3 boys in one day which can be determined by finding the efficiency as below,
$=\dfrac{x}{3\times 22}\ldots \ldots \ldots \left( iii \right)$
Now we have to add the expressions (i), (ii) and (iii) as we know that is to find the efficiency of all the people in one day. Hence,
$\Rightarrow \dfrac{x}{22}+\dfrac{x}{2\times 22}+\dfrac{x}{3\times 22}=1$
So, the LCM of the equation is,
$\begin{align}
  & \dfrac{2x+3x+6x}{132}=1 \\
 & \Rightarrow 11x=132 \\
 & \Rightarrow x=\dfrac{132}{11}=12 \\
 & \Rightarrow x=12\text{ days} \\
\end{align}$
So, the option B is correct.

Note: It is necessary to determine the work done by 1 man, 2 women or 3 boys in one day with the help as they all can do a piece of work in 22 days. To determine the efficiency of all the people which can be determined by finding the sum of all the work done in one day.