❍ Question -:
If 8 workers can build a wall in 12 days. How many days will it take 3 workers to build the same wall ?
❍ Explanation -:
In this question we are provided that 8 workers can finish a piece of work in 12 days. We are asked to calculate how many days it will take 3 workers to complete the same work.
We can solve this question using two methods :
- Unitary Method
- Method of proportion
[tex] \small \green{ \underline{ \underline{\bf{ Unitary \: Method}}}}[/tex]
8 workers can build a wall in 12 days
1 worker can build a wall in 12 × 8 days
3 workers can build a wall in [tex]\dfrac{12 × 8}{3}[/tex] = 32 days.
- Hence, If 8 workers can build a wall in 12 days. 3 workers will take 32 days to build the same wall.
[tex] \rule{47mm}{4pt}[/tex]
[tex] \small \orange{ \underline{ \underline{\bf{ Method \: of \: proportion }}}}[/tex]
Let us assume that 3 workers can build a wall in x days.
[tex] \begin{array}{ cc } \bf{Number \: of \: workers} & \bf{Number \: of \: days} \\ 8 &12 \\ 3&x \end{array}[/tex]
Ratio of workers = Inverse ratio of days
[tex] \small\sf{ 8 : 3 :: x : 12}[/tex]
Product of mean = Product of extreme
[tex] \rightarrow \small\rm{ 3 \times x = 8 \times 12}[/tex]
[tex] \rightarrow{x \: }\small\sf{ = \dfrac{8 \times 12}{3} = 32 \: days } [/tex]
- Hence, If 8 workers can build a wall in 12 days. 3 workers will take 32 days to build the same wall.
[tex] \rule{73mm}{5pt}[/tex]
