e other two Sides6,cottage industry produces a certain number of potte

1.	e other two Sides6,cottage industry produces a certain number of pottery articles in a day It was observerda particular day that the cost of production of each article (in rupees) was 3 more thance the number of articles produced on that day. Ifthe total cost of production on thatday was 90, find the number of articles produced and the cost of each article.
Answer» The total cost of production= Rs.90 Let the number of pottery articles produced bex.Therefore, cost of production of each article = Rs (2x+ 3) the total cost of production = no. ofpottery 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 orx= 6 As the number of articles produced can only be a positive integer, therefore, x can only be 6. Hence, number of articles produced = 6Cost of each article = 2 × 6 + 3 = Rs 15.

e other two Sides6,cottage industry produces a certain number of pottery articles in a day It was observerda particular day that the cost of production of each article (in rupees) was 3 more thance the number of articles produced on that day. Ifthe total cost of production on thatday was 90, find the number of articles produced and the cost of each article.

Answer»

The total cost of production= Rs.90

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

the total cost of production = no. ofpottery 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 orx= 6

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

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