A cottage industry produces a certain number of pottery articles in a ...
Problem Statement:
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of each article (in ₹) was 2 more than thrice the number of articles produced on that day. If the total cost of production on that day was ₹ 800, the number of articles produced was? Explain in details.
Solution:
Let us assume that the number of articles produced in a day be x and the cost of production of each article be y.
Given, the cost of each article is 2 more than thrice the number of articles produced on that day.
Therefore, y = 3x + 2.
Also, the total cost of production on that day was ₹ 800.
Therefore, xy = 800.
Substituting the value of y in the above equation, we get:
x(3x + 2) = 800
Expanding the above equation, we get:
3x² + 2x - 800 = 0
Using the quadratic formula, we get:
x = (-2 ± √(2² + 4(3)(800))) / (2(3))
x = (-2 ± √(6404)) / 6
x = (-2 ± 80) / 6
Therefore, x = 13.33 or x = -4.33.
As the number of articles produced cannot be negative, the number of articles produced in a day is 13.
Answer:
The number of articles produced in a day is 13.