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 Rs 750. The mathematical representation to find out the number of toys produced on that day is:

• A. x² – 50x + 320 = 0
• B. x² – 40x + 124 = 0
• C. x² – 45x+ 324 = 0
• D. x² – 55x+ 750 = 0

Answer 1

The correct option is D

x² – 55x+ 750 = 0

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

$x^2$ – $55x+750=0$ which is the required representation of the problem mathematically.