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

Answer: Option B

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