NIELIT 2016 DEC Scientist B - Section A: 59

Question

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

• A. $48$
• B. $32$
• C. $20$
• D. $16$

Answer 1

$\text{Let the required number of days be x.}$

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

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

$\Leftrightarrow$ $42*x$  $=$ $56*24$

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

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

$\textrm{Option B.}$

Answer 2

$\dfrac{MDH}{W} = \text{Constant}$

Where,

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

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

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