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 90, find the number of articles produced and the cost of each article ?

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Solution:

⇨Let the number of pottery articles produced be x

⇨Than price of pottery articles is = 2x+3

A/Q

x(2x+3)= 90

$A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was 90, find the number of articles produced and the cost of each article ?$
$\large \Rightarrow 2x^2+3x-90=0$

$\large \Rightarrow 2x^2+(15-12)x-90=0$

$\large \Rightarrow 2x^2+15x-12x-90=0$

$\large \Rightarrow 2x^2-12x+15x-90=0$

$\large \Rightarrow 2x(x-6)+15(x-6)=0$

$\large \Rightarrow (x-6)(2x+15)=0$

$\large \Rightarrow x-6=0,2x+15=0$

$\large \Rightarrow x=6,x=-\frac{15}{2}$

⇨x=-15/2, Number of articles never be negative or in fraction.

⇨Therefore number of articles = 6

⇨Price of articles = 2x+3 =2x6+3 = 15 Rs

Exercise 4.2

1. Find the roots of the following quadratic equations by factorisation:

(i) $x^2-3x-10=0$

(ii) $Find the roots of 2x^2+x-6=0 quadratic equations by factorization ?$

(iii) $Find the roots of \sqrt{2}x^2+7x+5\sqrt{2}=0 quadratic equations by factorization ?$

(iv) $Find the roots of 2x^2-x+\frac{1}{8}=0 quadratic equations by factorization ?$

(v) $\large 100x^{2}-20x+1=0$

3. Find two numbers whose sum is 27 and product is 182.

4. Find two consecutive positive integers, sum of whose squares is 365.

5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

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