₹480 is divided equally among 'x' children. If the number of children were 20 more, then each would have got ₹12 less . Find 'x'.

Number of children = x

Money recieved by each = $\dfrac{480}{x}$

If number of children were 20 more then money received by each child = $\dfrac{480}{x + 20}$

Given, if there are 20 more children then each will get ₹12 less

$\therefore \dfrac{480}{x} - \dfrac{480}{x + 20} = 12 \\[1em] \Rightarrow \dfrac{40}{x} - \dfrac{40}{x + 20} = 1 \text{ (Dividing the equation by 12) } \\[1em] \Rightarrow \dfrac{40(x + 20) - 40x}{x(x + 20)} = 1 \\[1em] \Rightarrow \dfrac{40x + 800 - 40x}{x^2 + 20x} = 1 \\[1em] \Rightarrow 800 = x^2 + 20x \\[1em] \Rightarrow x^2 + 20x - 800 = 0 \\[1em] \Rightarrow x^2 + 40x - 20x - 800 = 0 \\[1em] \Rightarrow x(x + 40) - 20(x + 40) = 0 \\[1em] \Rightarrow (x - 20)(x + 40) = 0 \\[1em] \Rightarrow x - 20 = 0 \text{ or } x + 40 = 0 \\[1em] x = 20 \text{ or } x = -40$

Since, number of children cannot be negative hence, x ≠ -40

∴ x = 20

Hence, number of children are 20.