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. $750$. Find the number of toys produced on that day.

• A. Number of toys are $40$.
• B. Number of toys are either $23$ or $46$.
• C. Number of toys are either $25$ or $30$.
• D. Number of toys are $15$.

Answer 1

The correct option is C Number of toys are either $25$ or $30$.

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

Therefore the cost of production of each toy that day = Rs. $(55-x)$

So the total cost of production that day = $x(55-x)$.

$x(55-x)=750$

$\Rightarrow -x^{{}^2}+55x-750=0$

$\Rightarrow x^2-55x+750=0$

$\Rightarrow x^2-25x-30x+750$

$\Rightarrow x(x-25)-30(x-25)=0$

$\Rightarrow (x-25)(x-30)=0$

So, $x=25$ or $x=30$

Therefore, the number of toys produced that day are $25$ or $30$.