Question

If ($x$+4) men can do a piece of work in ($x$+3) days, then find the number of days that ($x$+2) men will take for the same work.

• A. $\frac{(x^2+7x+8)}{(x+4)}days$
• B. $\frac{(x^2+9x+12)}{(x+2)}days$
• C. $\frac{(x^2+7x+12)}{(x+2)}days$
• D. $\frac{(2x^2+5x+12)}{(x+2)}days$

Answer 1

The correct option is C $\frac{(x^2+7x+12)}{(x+2)}days$

Given,
($x$+4) men can do a piece of work in ($x$+3) days.

We know that if the number of men increase, then the number of days taken to finish the piece of work will be less.

$\text{Number of men}\left(m\right)\propto \frac{1}{\text{Number of days}\left(d\right)}$
$\therefore \frac{m_1}{m_2}=\frac{d_2}{d_1}$

Given,
$m_1=(x+4)men$
$m_2=(x+2)men$
$d_1=(x+3)days$
$\text{and}{d}_2=\text{Number of days taken by (x+2) men}$
$\Rightarrow \frac{(x+4)}{(x+2)}=\frac{d_2}{(x+3)}$
$\Rightarrow d_2=\frac{(x+4)\times (x+3)}{(x+2)}$
$\Rightarrow d_2=\frac{(x^2+7x+12)}{(x+2)}days$