Question

Question 6 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 Rs 90, find the number of articles produced and the cost of each article.

Class 10 - Math - Quadratic Equations Page 76

Answer 1

Solution:

Given: The total cost of production= Rs.90

Let the number of pottery articles produced be x.
Therefore, cost of production of each article = Rs (2x + 3)      

the total cost of production = no. of  pottery articles produced × cost of production

A.T.Q

90.= x(2x + 3) = 0

⇒ 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 ⇒2x= - 15

⇒x= -15/2

 ⇒x – 6 = 0

⇒x=6

⇒ x = -15/2 or x = 6

As the number of articles produced can only be a positive integer, therefore, x can only be 6.

Hence, number of articles produced = 6
Cost of each article = 2 × 6 + 3 = Rs 15.

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Hope this will help you....

Answer 2

Let

in a day number of airticle produced = x

cost of every produced = ( 2x + 3 ) rupees

A/Q

x ( 2x + 3 ) = 90

=> 2x² + 3x - 90 = 0

=> 2x² - 12x + 15x - 90 = 0

=> 2x ( x - 6 ) + 15 ( x - 6 ) = 0

=> ( x - 6 ) ( 2x + 15 ) = 0

Either

x - 6 = 0 or 2x + 15 = 0

=> x = 6 => 2x = - 15

=> x = -15/2 ( impossible)

so , in a day number of produced is 6
.and Cost of every produced is ( 2 × 6 ) + 3 = 15

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