A frog was at the bottom of an 80m deep well. It attempted to come out of it by jumping. In each jump, it covered 1.15m but slipped down by 0.75m. The number of jumps after which it would be out of the well is:

Let's analyze the net distance covered by the frog in each jump and handle the final leap correctly:
Net distance covered in each non-final jump:

Net progress per jump=1.15m−0.75m=0.40m
The final jump:
On the very last jump, once the frog reaches or clears the top of the well (80m), it will not slip back down. The maximum height covered in the final jump is 1.15m.
Therefore, we subtract this final jump distance from the total depth to find the distance that must be covered by regular jump-and-slip cycles:

Remaining distance=80m−1.15m=78.85m
Number of initial jumps required:

Number of regular jumps=
0.40
78.85
​
=197.125
Since the number of jumps must be an integer, we round up to the next whole number, which gives 198 jumps.

Verify progress after 198 jumps:

Distance covered after 198 jumps=198×0.40m=79.2m
The remaining depth to reach the top is:

80m−79.2m=0.8m
On the next jump (199
th
jump), the frog can clear a distance of 1.15m. Since 1.15m≥0.8m, the frog successfully reaches the top and gets out of the well.

Total number of jumps required = 198+1=199.