A factory requires 63 days to produce a given number of articles by 42 machines. ____ machines would be required to produce the same number of articles in 54 days.

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A factory requires 63 days to produce a given number of articles by 42 machines. 49 machines would be required to produce the same number of articles in 54 days.Given that,Number of days required by 42 machines to produce a given number of article = 63 days.We have to find the number of machines that requires 54 days to produce the same number of articles.We know that two variables are said to be inversely proportional if and only if they are directly proportional to one another's reciprocal. If

x and y
   are two variables in inverse variations, then

xy=k, 
  where k is a proportionality constant.Here, if the number of days decreases, then the number of machines required to produce the same work will increase, so it is in the inverse proportion.Let us make a table as shown below:Number of days to complete the work

(x)
  Number of machines required

(y)

x
    1
   
   =63

y
    1
   
   =42

x
    2
   
   =54

y
    2
   
   =
  ?Using the relation of inverse proportion

x
    1

y
    1
   
   =
    x
    2

y
    2

, we get,

x
    1

y
    1
   
   =
    x
    2

y
    2

⇒
      y
      2
     
     =

x
        1

y
        1

x
        2

⇒
      y
      2
     
     =
      
       63×42
      
       54

∴
    y
    2
   
   =49
    Therefore, 49 machines would be required to produce the same number of articles in 54 days.

Number of days to complete the work $(x)$	Number of machines required $(y)$
$x 1 = 63$	$y 1 = 42$
$x 2 = 54$	$y 2 =$ ?

A factory requires 63 days to produce a given number of articles by 42 machines. ____ machines would be required to produce the same number of articles in 54 days.

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