A person is standing on the first step from the bottom of a ladder. If he has to climb 4 more steps to reach exactly the middle step, how many steps does the ladder have?

Correct Option (B)

The person is initially positioned on the 1st step of the ladder. To reach the middle step, the person climbs 4 additional steps. Therefore, the middle step is located at step number 1 + 4 = 5.

For a ladder with N steps, the middle step is given by the formula $$\frac{N+1}{2}$$, assuming N is an odd number to ensure a unique middle step. Equating the calculated middle step position with the formula:

$$5=\frac{N+1}{2}$$

Multiplying both sides by 2:

$$10=N+1$$

Subtracting 1 from both sides:

$$N=9$$

Thus, the ladder has 9 steps.

Incorrect Options:

If the ladder has 8 steps (Option A) or 10 steps (Option C), it contains an even number of steps. A ladder with an even number of steps does not possess a unique middle step, which contradicts the premise of the question implying a singular "middle step."

If the ladder has 11 steps (Option D), the middle step would be $$\frac{11+1}{2}=6$$th step. However, according to the problem, the person reaches the 5th step (1st step + 4 more steps) to arrive at the middle step. This contradicts the calculation for an 11-step ladder, where the middle step is the 6th step.