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Quadratic Equations
RD Sharma
CBSE
Grade 10

Question:

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.

Step-by-Step Solution

Key Concept: Articles $= x$, Cost $= 2x + 3$. $x(2x + 3) = 90 \Rightarrow 2x^2 + 3x - 90 = 0 \Rightarrow (2x + 15)(x - 6) = 0 \Rightarrow x = 6$. Cost $= 2(6) + 3 = ₹15$.
$x(2x + 3) = 90 \Rightarrow 2x^2 + 3x - 90 = 0$. [1.0 Mark]
$(2x + 15)(x - 6) = 0 \Rightarrow x = 6$ articles produced. [1.0 Mark]
Cost of each article $= 2(6) + 3 = ₹15$. [1.0 Mark]

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🎯 Official CBSE Marking Scheme:
Forming quadratic $2x^2 + 3x - 90 = 0$: 1.0 Mark
Solving $x = 6$ articles: 1.0 Mark
Finding cost $= ₹15$: 1.0 Mark

Correct Answer:
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