Monkey Climbing Pole Problem Analysis

This question presents a common type of aptitude problem that requires careful step-by-step calculation. We need to determine the total time a monkey takes to reach the top of a 30-metre pole, given its specific climbing and slipping pattern.

Understanding the Monkey's Movement Pattern

The monkey's movement is cyclical, occurring over two-minute intervals:

• First minute: The monkey climbs 15 metres upwards.
• Second minute: The monkey slips down 12 metres.

To understand the monkey's effective progress, we calculate the net height gained in one complete two-minute cycle:

Net climb in 2 minutes = $\text{Climb distance} - \text{Slipping distance}$

Net climb in 2 minutes = $15 \text{ metres} - 12 \text{ metres} = 3 \text{ metres}$

So, for every two minutes that pass, the monkey effectively gains 3 metres in height.

Calculating Time to Reach the Pole Top

A key insight for solving this type of problem is that the monkey stops slipping once it reaches the top of the pole. The final climb of 15 metres will take it to the top without any subsequent slip.

Therefore, we need to consider how much height the monkey needs to cover through its net gain cycles before the final, non-slipping climb. The pole height is 30 metres, and the final climb is 15 metres. So, the height to be covered before the last climb is:

Height to cover before final climb = $\text{Total pole height} - \text{Final climb distance}$

Height to cover before final climb = $30 \text{ metres} - 15 \text{ metres} = 15 \text{ metres}$

Now, let's calculate how many 2-minute cycles are needed to cover these 15 metres:

Number of cycles = $\frac{\text{Height to cover before final climb}}{\text{Net climb per cycle}}$

Number of cycles = $\frac{15 \text{ metres}}{3 \text{ metres/cycle}} = 5 \text{ cycles}$

The total time taken for these 5 cycles is:

Time for 5 cycles = $\text{Number of cycles} \times \text{Time per cycle}$

Time for 5 cycles = $5 \times 2 \text{ minutes} = 10 \text{ minutes}$

After 10 minutes, the monkey has climbed a total net height of 15 metres and is positioned at 15 metres from the ground.

Now, we consider the 11th minute:

• At the beginning of the 11th minute (after 10 minutes have passed), the monkey is at a height of 15 metres.
• In the 11th minute, the monkey makes its next climb, which is 15 metres upwards.
• Total height reached at the end of the 11th minute = Current height + Climb in 11th minute
• Total height reached = $15 \text{ metres} + 15 \text{ metres} = 30 \text{ metres}$

At this point, the monkey has reached the very top of the 30-metre pole. Since it has achieved its goal, it will not slip down again, and the process concludes.

Final Time Calculation Summary

The progression of the monkey's climb can be clearly seen in the following table:

The table clearly illustrates that the monkey reaches the 30-metre mark at the end of the 11th minute. Therefore, the total time required is 11 minutes.