Question

If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man or 1 woman or 1 boy in_______
A. $21$days
B. $24$ days
C. $26$ days
D. $33$ days

Answer 1

Hint: According to the question we have to determine the time to complete a piece of work can be done by 1 man or 1 woman or 1 boy when 1 man or 2 women or 3 boys can do a piece of work in 44 days. So, first of all we have to let the same piece of work be done by 1 man or 1 woman or 1 boy in $x$ days.
Now, we have to determine the work done by 1 man in one day which can be determine by finding the efficiency and same as we have to determine the work done by 2 women in one day which can be determine by finding the efficiency and same as determine the work done by 3 boys in one day which can be determine 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 of the work done in one day.

Complete step-by-step solution:
Step 1: First of all we have to let the same piece of work be done by 1 man or 1 woman or 1 boy in $x$ days as mentioned in the solution hint.
Step 2: Now, we have to determine the work done by 1 man in one day which can be determine by finding the efficiency as below:
$ = \dfrac{x}{{44}}$……………….(1)
Step 2: Now, we have to determine the work done by 2 women in one day which can be determine by finding the efficiency as below:
$ = \dfrac{x}{{2 \times 44}}$…………….(2)
Step 3: Now, we have to determine the work done by 3 boys in one day which can be determine by finding the efficiency as below:
$ = \dfrac{x}{{3 \times 44}}$…………….(3)
Step 4: Now, we have to add the expression (1),(2), and (3) as mentioned in the solution hint which is the efficiency of all the people in one day. Hence,
$ \Rightarrow \dfrac{x}{{44}} + \dfrac{x}{{88}} + \dfrac{x}{{132}} = 1$
Now, to find the value of x we have to solve the L.C.M of the equation as obtained just above,
$
   \Rightarrow \dfrac{{6x + 3x + 2x}}{{264}} = 1 \\
   \Rightarrow 11x = 264 \\
   \Rightarrow x = \dfrac{{264}}{{11}} \\
   \Rightarrow x = 24days
 $
Final solution: Hence, time to complete a piece of work can be done by 1 man or 1 woman or 1 boy is 24 days when 1 man or 2 women or 3 boys can do a piece of work in 44 days.

Therefore option (B) is correct.

Note: It is necessary to determine the work done by 1 man or 2 women or 3 boys in one day with the help of as they all can do a piece of work in 44 days.
To determine the efficiency of all the people which can be determined by finding the sum of all of work done in one day.