A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ 90, find the number of articles produced and the cost of each article.
Solution:
Let the number of articles produced in one day be x.
Therefore, the cost (in rupees) of each article will be (3 + 2x)
The total cost of production = Cost of each article × Total number of articles
Let us use this relation to form a quadratic equation.
(3 + 2x) ( x) = 90
3x + 2x2 = 90
2x2 + 3x - 90 = 0
2x2 + 15x - 12x - 90 = 0
x(2x + 15) - 6(2x + 15) = 0
(2x + 15) (x - 6) = 0
2x + 15 = 0 and x - 6 = 0
2x = -15 and x = 6
x = -15/2 and x = 6
Number of articles cannot be a negative number.
Therefore, x = 6
Cost of each article = 3 + 2x
= 3 + 2 (6)
= Rs.15
Cost of each article is Rs.15.
Number of articles produced is 6.
☛ Check: NCERT Solutions Class 10 Maths Chapter 4
Video Solution:
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was ₹ 90, find the number of articles produced and the cost of each article
Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 6
Summary:
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the cost of the production on that day is ₹ 90 then the number of articles produced and the cost of production is 6 and Rs.15 respectively.
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