Question : If $x$ men can do a piece of work in $x$ days, then the number of days in which $y$ men can do the same work is:
Option 1: $xy$ days
Option 2: $\frac{y^{2}}{x}$ days
Option 3: $\frac{x^{2}}{y}$ days
Option 4: $x^{2}y$ days
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Correct Answer: $\frac{x^{2}}{y}$ days
Solution :
Given: $x$ men can do a piece of work in $x$ days.
We know the concept $M_1D_1=M_2D_2$, where $M_1$, $M_2$ are the persons and $D_1$, $D_2$ are the number of days.
According to the question,
⇒ $x×x=y×D_2$
$\therefore D_2=\frac{x^{2}}{y}$ days
Hence, the correct answer is $\frac{x^{2}}{y}$ days.
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