If ‘m’ workers working ‘m’ hours a day for each of ‘m’ days produce ‘m’ units of work, then the unit of work produces by ‘n’ workers working ‘n’ hours a day for each of ‘n’ days is?
If ‘m’ workers working ‘m’ hours a day for each of ‘m’ days produce ‘m’ units of work, then the unit of work produces by ‘n’ workers working ‘n’ hours a day for each of ‘n’ days is?
1). \(\frac{{{m^2}}}{{{n^{2}}}}\)
2). \(\frac{{{n^3}}}{{{m^2}}}\)
3). \(\frac{{{m^2}}}{{{n^3}}}\)
4). \(\frac{{{n^2}}}{{{m^3}}}\)
1 answers
We can use the formula:
$(\frac{{{\rm{M}} \times {\rm{E}} \times {\rm{T}} \times {\rm{D}}}}{W} = constant)$
Where M = no. of workers working
E = efficiency of each worker
D = no. of working days.
T = working hours / day
W = net work done.
So we can write,
$(\Rightarrow \frac{{{M_1} \times {E_1} \times {T_1} \times {D_1}}}{{{W_1}}} = \frac{{{M_2} \times {E_2} \times {T_2} \times {D_2}}}{{{W_2}}})$ _________(1)
Given In the question:
‘m’ workers working m hours a day for each of m days produce m units of work
∴ M1 = m workers, E1 = E, D1 = m days, T1=m hours, W1 = m units.
[Assuming efficiency of each worker = E]
Putting the values in equation (1) we get,
$(\Rightarrow \frac{{{M_2} \times {E_2} \times {T_2} \times {D_2}}}{{{W_2}}} = {m^2}E)$ ___________(2)
Assume that when n workers working n hours a day for each of n days, work done = W units.
Substituting the values in equation (2) we get,
$(\begin{array}{l} \Rightarrow \frac{{n \times E \times n \times n}}{W} = {m^2}E\\ \Rightarrow W = \frac{{{n^3}}}{{{m^2}}}units \end{array})$