The total cost price of a certain number of identical articles is ₹ 4800. By selling the articles at ₹ 100 each, a profit equal to the cost price of 15 articles is made. Find the number of articles bought.

Let no. of articles bought be x.

C.P. of each article = ₹ $\dfrac{4800}{x}$

Profit earned = ₹ $15 \times \dfrac{4800}{x}$

We know that,

Profit = S.P. - C.P.

$\Rightarrow \dfrac{72000}{x} = 100x - 4800 \\[1em] \Rightarrow 72000 = x(100x - 4800) \\[1em] \Rightarrow 72000 = 100(x^2 - 48x) \\[1em] \Rightarrow 720 = x^2 - 48x \\[1em] \Rightarrow x^2 - 48x - 720 = 0 \\[1em] \Rightarrow x^2 - 60x + 12x - 720 = 0 \\[1em] \Rightarrow x(x - 60) + 12(x - 60) = 0 \\[1em] \Rightarrow (x + 12)(x - 60) = 0 \\[1em] \Rightarrow x = -12 \text{ or } x = 60.$

Since, no. of articles cannot be negative,

∴ x ≠ -12.

Hence, no. of articles bought = 60.