Mr. Mehra sends his servant to the market to buy oranges worth ₹ 15. The servant having eaten three oranges on the way, Mr. Mehra pays 25 paise per orange more than the market price. Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.

No. of oranges Mr. Mehra receives = x

Total no. of oranges = x + 3

Actual cost of each orange = $\dfrac{15}{x + 3}$

Cost of one orange for Mr. Mehra = $\dfrac{15}{x}$

According to question,

$\Rightarrow \dfrac{15}{x} - \dfrac{15}{x + 3} = \dfrac{25}{100} \\[1em] \Rightarrow \dfrac{15(x + 3) - 15x}{x(x + 3)} = \dfrac{1}{4} \\[1em] \Rightarrow \dfrac{15x + 45 - 15x}{x^2 + 3x} = \dfrac{1}{4} \\[1em] \Rightarrow \dfrac{45}{x^2 + 3x} = \dfrac{1}{4} \\[1em] \Rightarrow 180 = x^2 + 3x \\[1em] \Rightarrow x^2 + 3x - 180 = 0 \\[1em] \Rightarrow x^2 + 15x - 12x - 180 = 0 \\[1em] \Rightarrow x(x + 15) - 12(x + 15) = 0 \\[1em] \Rightarrow (x + 15)(x - 12) = 0 \\[1em] \Rightarrow x + 15 = 0 \text{ or } x - 12 = 0 \\[1em] \Rightarrow x = -15 \text{ or } x = 12.$

Since, no. of oranges cannot be negative,

∴ x ≠ -15.

Hence, no. of oranges = 12 and equation = x² + 3x - 180.