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 on 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.

Answer 1

Answer:

Step-by-step explanation:

SOLUTION:

Given: The total cost of production= ₹ 90

Let the number of pottery articles produced be x.

Therefore, cost of production of each article = ₹ (2x + 3)      

The total cost of production = number 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

⇒ (2x + 15) = 0  or (x – 6) = 0

⇒2x= - 15  or 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 = ₹ 15.

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Answer 2

The totɑl cost of production= Rs.90

Let the number of pottery ɑrticles produced be x.
Therefore, cost of production of eɑch ɑrticle = Rs (2x + 3)      

the totɑl cost of production = no. of  pottery ɑrticles produced × cost of production

ɑ.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

ɑs the number of ɑrticles produced cɑn only be ɑ positive integer, therefore, x cɑn only be 6.


Hence, number of ɑrticles produced = 6
Cost of eɑch ɑrticle = 2 × 6 + 3 = Rs 15.

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