The cost of an article is ₹ 3 more than twice the total number of articles. If the cost of all the articles is ₹ 189, then the number of articles is :

1. 7

2. 9

3. 11

4. 13

Let the total number of articles be x and the cost of each article be y.

Given,

The cost of an article is ₹ 3 more than twice the total number of articles.

⇒ y = 2x + 3     ………(1)

Given,

Total cost of all articles = ₹ 189.

⇒ xy = 189     ………(2)

Substituting value of y from equation (1) in equation (2), we get :

⇒ x(2x + 3) = 189

⇒ 2x² + 3x = 189

⇒ 2x² + 3x - 189 = 0

⇒ 2x² - 18x + 21x - 189 = 0

⇒ 2x(x - 9) - 21(x - 9) = 0

⇒ (2x - 21)(x - 9) = 0

⇒ (2x - 21) = 0 or (x - 9) = 0     [Using zero -product rule]

⇒ 2x = 21 or x = 9

⇒ x = $\dfrac{21}{2}$ or x = 9

Since, the number of articles cannot be in fraction, thus x ≠ $\dfrac{21}{2}$.

Hence, option 2 is the correct option.