A cottage industry produces a certain number of potteries in a day. It was found that the cost of production of each article rs5 more than twice the number of potteries prduced in the day. If the cost of production on that day was rs168. Find the number of potteries prduced
Answers
Answer:
Step-by-step explanation:
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Answer:
No. of potteries produced = 8
Step-by-step explanation:
Let the cost of production of one article in Rupees = x
Let the number of articles produced in the day = y
Total cost of production =
Cost of production of one article * No. of articles produced
=> Cost of production = xy .........(i)
ATQ, Cost of production of one article is 5 more than twice the number of articles produced
=> x is 5 more than 2y
=> x = 2y + 5 ........(ii)
ATQ, total cost of production on that day = 168
Using (i), we get:
xy = 168 ...........(iii)
We need to now solve (ii) and (iii) to get the unknowns "x" and "y"
From (iii), x = 168/y
Substituting this in (ii), we get:
168/y = 2y + 5
=> 168 = 2y² + 5y
=> 2y² + 5y - 168 = 0
=> 2y² -16y + 21y - 168 = 0
=> 2y(y - 8) +21 (y - 8) = 0
=> (2y + 21)(y - 8) = 0
=> y = -21/2 or y = 8
As "y" stands for number of articles, negative values are inadmissible.
=> y = 8
Answer: No. of potteries produced = y = 8
Now to find x:
Substituting for y in (i), we get:
x = 168/8 = 21
=> x = 21
Cost per article in Rupees = 21
Verification:
x = cost of production of one article in Rupees = 21
y = no. of articles produced = 8
Total cost of production = 21*8 = 168 (verified)
Also,
21 is 5 more than 2*8
=> Cost of production per article is 5 more than twice the number of articles produced. (Condition stated in problem description fulfilled)