An algebra problem by Ashtik Mahapatra

Since m men do it in d days , one man will do it in mXd days and so m+r will do it in

mXd/m+r Ans

K.K.GARG,India

We know that if $m$ men can do the work in $d$ days, then if $m+r$ men will do the work, the amount of time to complete the work will decrease. This is an application of inverse variation, with the formula $y$ = $\frac {k}{x}$ . $y$ and $x$ here are quantities and $k$ is called the constant of variation.

To solve the problem, first we let $y = m$ and $x = d$ to find $k$ .

$m$ = $\frac {k}{d}$

$md = k$

Next, we use $y$ = $\frac {k}{x}$ again . We let $x = d$ , $k = md$ and $y = m + r$ and we solve for $d$ .

$m + r$ = $\frac {md}{d}$

$\boxed{\frac {md}{m + r}}$ = $d$

Thus the answer.

m+r=md/d d=md/(m+r)