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$56$ men can complete a piece of work in $24$ days. In how many days can $42$ men complete the same piece of work ?

  1. $48$
  2. $32$
  3. $20$
  4. $16$
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$\text{Let the required number of days be x.}$

$\text{Less men, More days (Indirect proportion)}$

$\therefore$ $\text{ $42$ : $56$ :: $24$ : x}$

$\Leftrightarrow$ $42*x$  $=$ $56*24$

$\Leftrightarrow$       $x$       $=$  $(\frac{56*24}{42}​)​​​​​​$   

$\Leftrightarrow$       $x$       $=$   $32$

$\textrm{Option B.}$
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$\dfrac{MDH}{W} = \text{Constant}$

Where,

  • $M =$ Number of men
  • $D =$ Number of days
  • $H =$ Number of hours per day
  • $W =$ Amount of work

Now, $\dfrac{56\;\text{men} \times 24\;\text{days}}{W} = \dfrac{42\;\text{men} \times D}{W}$ 

$\implies D = 32\;\text{days}.$

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