Find the whole number which when increased by 20 is equal to 69 times the reciprocal of the number.

Let the required number be x
Then,
$$\eqalign{ & \Leftrightarrow x + 20 = \frac{{69}}{x} \cr & \Leftrightarrow {x^2} + 20x - 69 = 0 \cr & \Leftrightarrow {x^2} + 23x - 3x - 69 = 0 \cr & \Leftrightarrow x\left( {x + 23} \right) - 3\left( {x + 23} \right) = 0 \cr & \Leftrightarrow \left( {x + 23} \right)\left( {x - 3} \right) = 0 \cr & \Leftrightarrow x = 3\,\,\,\,\,\,\,\,\,\left[ {\because x \ne - 23} \right] \cr} $$