A frog tries to come out of a dried well 4.5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well?

The correct option is 29 (Option 2).

Step-by-Step Explanation:

1. Understand the parameters:
Total depth of the well = 4.5 m = 450 cm.
Distance covered in one jump upwards = 30 cm.
Distance slipped back after each jump = 15 cm.
Net distance covered in one full jump-and-slide attempt (except the final jump) = 30 cm - 15 cm = 15 cm.

2. Consider the final jump:
On the very last jump, once the frog reaches or crosses the top edge of the well (the remaining 30 cm), it successfully escapes and does not slide down. Therefore, we subtract the final jump distance of 30 cm from the total depth first.

$\text{Remaining depth before final jump}=450\text{cm}-30\text{cm}=420\text{cm}$

3. Calculate jumps needed to cover the initial 420 cm:
Since each jump results in an effective progress of 15 cm:

$\text{Number of jumps}=\frac{420}{15}=28\text{jumps}$

4. Add the final jump:
After 28 jumps, the frog is at a height of 420 cm. With the 29th jump, the frog covers the remaining 30 cm and reaches the top (420 cm + 30 cm = 450 cm), coming out of the well without sliding back.

$\text{Total number of jumps required}=28+1=29$