Question

39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons working 6 hours a day complete the work.

Answer 1

The given sum can be formatted into the three following columns

$\begin{array}{ccc}Persons& Days& Hours/Day\\ 39& 12& 5\\ 30& ?& 6\end{array}$

Since the variations exist in all the three columns, we proceed step by step.

We freeze the first column

$\begin{array}{ccc}Persons& Days& Hours/Day\\ 39& 12More& 5Less\\ 39& xLess& 6More\end{array}$

This is a clear case of inverse variation. In inverse variation, rows across get multiplied and equated.

$12\times 5=6\times x$

$(12\times 5)÷6=x$

$\Rightarrow 10=x$

Now the second step:We freeze the hours per day column and proceed with the other two columns. We see that the variation now lies between these two columns.This is also a clear case of inverse variation.

$\begin{array}{ccc}No.ofPersons& NoofDays& Hours/Day\\ 39More& 10Less& 6\\ 30Less& yMore& 6\end{array}$

So we have

$39\times 10=30\times y$

$\frac{(39\times 10)}{30}=y$

$13=y$

Hence 13 days is the answer.