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 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.

Answer 1

x=6 and y=15

No. of articles produced i.e. x = 30 and cost of production of each article i.e. y is 15.

•let no. of articles produced = x

•let cost of production of each article

=y

•According to question

y=2x+3 ___(1)

•also, total cost of production = no. of

toys × cost of each article

•90= xy____(2)

•multiply (1) by x

•xy= 2x²+3x

•90= 2x²+3x

•2x²+3x-90=0

•2x²+15x-12x+90=0

•x(2x+15)-6(2x+15)=0

•(x-6)(2x+15)=0

•x=6 or x=-15/2

=•x=30 (as no. of articles can never

be negative)

•y=15

Answer 2

The number of articles is 6

The cost of each article is Rs 15  

Step-by-step explanation:

Given as :

A cottage industry produces a certain number of pottery articles in a day.

Let the number of article produced = n

Let The cost of each article = Rs x

Total cost of production = Rs 90

According to question

The cost of production of each article was 3 more than twice the number of articles produced on that day .

i.e x = 2 n + 3               ..........1

Again

Total cost of production = no. of  article × cost of each article

i.e  Rs 90 = n × Rs x

Or, n x = 90                .........2

Solving eq 1 and eq 2

x = 2 n + 3  

i.e  n ( 2 n + 3 ) = 90

Or, 2 n² + 3 n - 90 = 0

Solving this quadratic eq , we get

Or, 2 n² -12 n + 15 n - 90 = 0

Or, 2 n ( n - 6 ) + 15 ( n - 6 ) = 0

Or, ( n- 6 ) + ( 2 n + 15 ) = 0

i.e ( n - 6 ) = 0         ,  ( 2 n + 15 ) = 0

∴    n = 6             , n = $\dfrac{-15}{2}$ = - 7.5

So, The number of articles = n = 6

Put the value of n in eq 2

∵ n x = 90

Or, 6 x = 90

∴       x = $\dfrac{90}{6}$

i,e     x = Rs 15

So, The cost of each article = x = Rs 15

Hence, The number of articles is 6

And The cost of each article is Rs 15   . Answer