High School

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------------------------------------------------ It takes 8 workers 12 days to build a wall. Work out how many days it would take 3 workers to complete the same job.

Answer :

Answer: 4.5 days or 4 1/2 days

Step-by-step explanation: We can use cross product property, to solve this. Workers to Days remember that

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]