Question

Two persons could fit new windows in the house in $3$ days.

(i) One of the persons fell ill before the work started. How long would the job take now?

(ii) How many persons would be needed to fit the windows in one day?

Answer 1

(i) Let the number of days required by $1$ man (as $1$ person fell ill) to fit all the windows be $x.$ The following table is obtained.

$\begin{array}{ccc}\text{Number of persons}& 2& 1\\ \text{Number of days}& 3& x\end{array}$

Lesser the number of persons more will be the number of days required to fit all the windows. Hence, this is a case of inverse proportion. Therefore,

$2\times 3=1\times x$

$\therefore x=6$

Hence, the number of days taken by $1$ man to fit all the windows is $6.$

(ii) Let the number of persons required to fit all the windows in one day be \(y.\) The following table is formed.

$\begin{array}{ccc}\text{Number of persons}& 2& y\\ \text{Number of days}& 3& 1\end{array}$

Lesser the number of days more will be the number of persons required to fit all the windows. Hence, this is a case of inverse proportion. Therefore,

$2\times 3=y\times 1$

$\therefore y=6$

Hence, $6$ persons are required to fit all the windows in one day.