Ex 4.2 Q6 - 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,
No. of articles produced = x
➙ It is given that the cost of production of each article (in rupees) on a particular day was 3 more than twice the number of articles produced on that day,
∴ Cost of production of each article
= ₹ (2x + 3)
∴ Total cost of production = ₹ x(2x + 3)
*But according to question, the total cost of production on that day was ₹ 90,
∴ x(2x + 3) = 90
∴ 2x² + 3x = 90
∴ 2x² + 3x - 90 = 0
*Although you can use any method for solving this quadratic equation i.e Factorization method, Completing the square method, or Quadratic formula.
Here we'll use Factorization method as it is very easy and less time consuming..
∴ 2x² + 3x - 90 = 0
∴ 2x² + 15x - 12x - 90 = 0
∴ x(2x + 15) - 6(2x + 15) = 0
∴ (2x + 15) (x - 6) = 0
Now,
2x + 15 = 0 OR x - 6
∴ 2x = -15 ∴ x = 6
∴ x =
-15
/
2
But, x can't be negetive as it is no. of articles produced,
∴ x = 6
Therefore,
*No. of articles produced
= x
= 6
*Cost of each article
= 2x + 3
= 2(6) + 3
= 12 + 3
= ₹ 15
Hence,
The number of articles produced is 6 and cost of each article is ₹15.
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Try This..
✒ A factory produces ‘x’ toys a day. The cost of each toy is ₹5 more than the number of toys produced. Total cost is ₹400. Find x.
✒ The sum of the reciprocals of two numbers is 1/6, and their product is 8. Find the numbers.
✒ The product of two consecutive positive integers is 132. Find the integers.
❌ Common Mistakes
Forgetting to bring the equation to standard form:▸ Always rearrange the equation to ax² + bx + c = 0 before solving.Ignoring the negative root:▸ Always check which root is valid in the context of the problem.▸ Negative values usually don't make sense in physical quantities like articles.Errors in applying the quadratic formula:▸ Be extra careful with signs when plugging into the formula.▸ A single minus can mess it all up.Skipping verification:▸ Plug your value of x back into the original equation to make sure it really gives you ₹90 as the total cost.
📝 Related Questions:-
Queries Solved:-
Class 10 Ex 4.2
Ex 4.2 Q6 Class 10
Class 10 Ex 4.2 Q6
Class 10 Chap 4 Ex 4.2 Q6
Class 10 Quadratic Equations
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