An employer finds that if he increases the weekly wages of each worker by ₹ 5 and employs five workers less, he increases his weekly wage bill from ₹ 3150 to ₹ 3250. Taking the original weekly wage of each worker as ₹ x; obtain an equation in x and then solve it to find the weekly wages of each worker.

Initial weekly wage = ₹ 3150,

Let weekly wage of each worker be ₹ x,

No. of employees = $\dfrac{3150}{x}$

New wage = ₹ (x + 5)

No. of employees after reducing 5 employees = $\dfrac{3150}{x}$ - 5

Given, new total wage = ₹ 3250

$\Rightarrow (x + 5)\Big(\dfrac{3150}{x} - 5\Big) = 3250 \\[1em] \Rightarrow (x + 5)\Big(\dfrac{3150 - 5x}{x}\Big) = 3250 \\[1em] \Rightarrow \dfrac{(x + 5)(3150 - 5x)}{x} = 3250 \\[1em] \Rightarrow 3150x - 5x^2 + 15750 - 25x = 3250x \\[1em] \Rightarrow 5x^2 + 3250x - 3150x + 25x - 15750 = 0 \\[1em] \Rightarrow 5x^2 + 125x - 15750 = 0 \\[1em] \Rightarrow 5(x^2 + 25x - 3150) = 0 \\[1em] \Rightarrow x^2 + 25x - 3150 = 0 \\[1em] \Rightarrow x^2 + 70x - 45x - 3150 = 0 \\[1em] \Rightarrow x(x + 70) - 45(x + 70) = 0 \\[1em] \Rightarrow (x - 45)(x + 70) = 0 \\[1em] \Rightarrow x - 45 = 0 \text{ or } x + 70 = 0 \\[1em] \Rightarrow x = 45 \text{ or } x = -70.$

Since wage cannot be negative,

∴ x ≠ -70.

Hence, weekly wage of worker = ₹ 45 and quadratic equation = x² + 25x - 3150 = 0.