Question

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be ₹55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. Calculate the number of toys produced on that day. Select the possible answers.

• A. 20
• B. 30
• C. 15
• D. 25

Answer 1

Answer: (B), (D)

The correct options are
B

30

D

25

Let the number of toys produced on that day be $x$.

$\therefore$ The cost of production (in rupees) of each toy that day = ₹ $(55–x)$.

So, the total cost of production (in rupees) that day = $x\times (55-x)$.

$\therefore$ $x\times (55-x)=750$

$\Rightarrow$ $55\left(x\right)$ – $x^2=750$

$\Rightarrow$ $-x^2$ + $55x–750=0$

$\Rightarrow$ $x^2$ – $55x+750=0$

$\therefore$ The number of toys produced that day satisfies the quadratic equation.

$x^2–55x+750=0$
$x^2–30x-25x+750=0$
$x(x-30)-25(x-30)=0$
$(x-30)(x-25)=0$

Solving, we get x = 30 or 25