☯ Appropriate Question -:
If 20 workers can build a school in 18 days, how many days will it take 12 workers to build the same school?
☯ Explanation -:
In this question we are provided that 20 workers can build a school in 18 days. We are asked to calculate how many days will 12 workers will take to do the same work.
We can solve this question using two methods :
- Unitary Method
- Method of proportion
[tex] \small\bf{ Unitary \: Method}[/tex]
20 workers can build a school in 18 days
1 worker can build a school in 20 × 18 days
12 workers can build a school in [tex]\dfrac{20 × 18 }{12}[/tex] = 30 days.
- Hence the required number of days is 30.
[tex] {{\rule{40mm}{4pt}}}[/tex]
[tex] \small\bf{ Method \: of \: proportion }[/tex]
Let us assume that 12 workers can finish the work in x days.
[tex]\begin{array}{c|c} \bf{Number \: of \: workers }& \bf{Number \: of \: days}\\ 20 & 18 \\ 12 & x\end{array}[/tex]
Ratio of workers = Inverse ratio of days
[tex] \small\sf{ 20 : 12 :: x : 18}[/tex]
Product of mean = Product of extreme
[tex] \small\rm{ 12 \times x = 20 \times 18}[/tex]
[tex] \small \rm{ \dfrac{20 \times 18}{12} = 30 \: days}[/tex]
- Hence the required number of days is 30.
[tex] \rule{72mm}{5pt}[/tex]
