Step-by-step explanation:

Correct option is A)

⇒ Let the number of toys produced on that day be x

⇒ Given that The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day

∴ The cost of production of each toy that day =Rs.(55–x)

⇒ So that total cost of production that day =Rs.x(55–x)

⇒ Given that On a particular day, the total cost of production was Rs.750.

∴ x(55−x)=750

⇒ 55x–x

2

=750

⇒ x

2

−55x+750=0

∴ We can see, equation given in question is correct.

Answer:

[tex]\qquad\qquad\boxed{ \sf{ \: \bf \: {x}^{2} - 55x + 750 = 0 \: }}\\ \\ [/tex]

Step-by-step explanation:

Given that,

• A cottage industry produce a certain number of toys in a day.

• The cost of production of each toy (in rupee) was found to be 55 minus the number of articles produced in a day.

• On a particular day, the total cost of production was Rs 750.

Now,

• x denotes the number of toys production on that day.

So, According to statement,

[tex]\sf \: Cost \: of \: production \: of \: 1 \: toy \: = \: 55 - x \\ \\ [/tex]

So,

[tex]\sf \: Cost \: of \: production \: of \: x \: toys\: = \: x(55 - x) \\ \\ [/tex]

As it is given that,

[tex]\sf \: Total \: cost \: of \: production \: of \: x \: toys\: = \: 750 \\ \\ [/tex]

So,

[tex]\sf \: x(55 - x) = 750 \\ \\ [/tex]

[tex]\sf \: 55x - {x}^{2} = 750 \\ \\ [/tex]

[tex]\sf\implies \sf \: {x}^{2} - 55x + 750 = 0 \\ \\ [/tex]

[tex]\rule{190pt}{2pt}[/tex]

Additional Information

[tex]\begin{gathered}\: \: \: \: \: \: \begin{gathered}\begin{gathered} \footnotesize{\boxed{ \begin{array}{cc} \small\underline{\frak{\pmb{{More \: identities}}}} \\ \\ \bigstar \: \bf{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} }\:\\ \\ \bigstar \: \bf{ {x}^{2} - {y}^{2} = (x + y)(x - y)}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} - {(x - y)}^{2} = 4xy}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2})}\:\\ \\ \bigstar \: \bf{ {(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}\:\\ \\ \bigstar \: \bf{ {(x - y)}^{3} = {x}^{3} - {y}^{3} - 3xy(x - y) }\:\\ \\ \bigstar \: \bf{ {x}^{3} + {y}^{3} = (x + y)( {x}^{2} - xy + {y}^{2} )}\: \end{array} }}\end{gathered}\end{gathered}\end{gathered}[/tex]