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 ) was 3 more than twice the number of
articles produced on that day. If the total cost of
production on that day was 90, then find the
number of articles produced and the cost of each
article.
Answers
ANSWER
Let there be x articles.
Then the production cost of each article =3+2x
Total production cost =x(3+2x)=90
3x+2x
2
=90
2x
2
+3x−90=0
2x
2
+15x−12x−90=0
2x(x−6)+15(x−6)=0
(2x+15)(x−6)=0
x=6,−
2
15
Number cannot be negative.
So, number of articles =6 and the cost of each article =Rs.15
Step-by-step explanation:
we know that
total cost of production = no. of articles produced×cost of article ----------(i)
given total cost of production = Rs 90
and
cost of production to each article was 3 more than twice the number of articke produced that day
let the number of articles be x
hence
cost of articles =2x+3
from eq.(i)
90=x(2x+3)
2x²+3x=90
2x²+3x-90=0
factorizing the above equation we get ......
2x²+15x-12x-90=0
x(2x+15)-6(2x+15)=0
(x-6)(2x+15)=0
so
x= 6 or -15/2
since x can't be negative as number of article cannot be negative so we can say that
.
number of articles =6
cost of articles=2x+3
=(2×6)+3= 15...
therefore .....the answer is Rs 15 .........
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i hope the solution was helpul to you .......
thank you.