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. We would like to find out the number of toys produced on that day.​

Answer 1

Answer:

Toys produced on that days is 25 or 30.

Step-by-step explanation:

⇒Let us say, number of toys produced in a day be x.

⇒Therefore, cost of production of each toy = Rs(55 – x)

⇒Given, total cost of production of the toys = Rs 750

⇒∴ x(55 – x) = 750

⇒ x² – 55x + 750 = 0

⇒ x² – 25x – 30x + 750 = 0

⇒ x(x – 25) -30(x – 25) = 0

⇒ (x – 25)(x – 30) = 0

Thus, either x - 25 = 0 or x – 30 = 0

⇒ x = 25 or x = 30

Hence, the number of toys produced in a day, will be either 25 or 30.

Answer 2

Given :

• The cost of production of each toy is equal to 55 minus the number of toys produced in a day
• On a particular day, total cost of production was 750

To find :

• Number of toys produced in that day

Solution :

Let the number of toys produced in that day be y

∴ Cost of production of each toy = 55 - y

∴ Cost of total production = y(55 - y)

So according to question,

$\longmapsto\sf y(55 - y) = 750 \\\\ \\ \longmapsto\sf 55y - y^2 = 750 \\\\ \\ \longmapsto\sf -(y^2 - 55y + 750) = 0 \\\\ \\ \longmapsto\sf y^2 - 55y + 750 = 0 \\\\ \\ \longmapsto\sf y^2 - 30y - 25y + 750 = 0 \\\\ \\ \longmapsto\sf y(y - 30) - 25(y - 30) = 0 \\\\ \\ \longmapsto\sf (y - 25)(y - 30) = 0 \\\\ \\ \longmapsto\boxed{\underline{\overline{\bf{\mid{y = 25 \ \ or \ \ y = 30 \mid}}}}}$

∴ Number of toys produced in that day = 25 or 30