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

Options

A. 200
B. 198
C. 201
D. 199

Answer

To solve the problem of how many jumps the frog needs to make to get out of an 80 m deep well, we can break it down into a step-by-step solution.

### Step 1: Determine the net distance covered in one jump.
The frog jumps up 1.15 m but slips back 0.75 m after each jump. Therefore, the net distance covered in one jump can be calculated as follows:

\[ \text{Net distance per jump} = \text{Jump height} - \text{Slip back} = 1.15 \, \text{m} - 0.75 \, \text{m} = 0.4 \, \text{m} \]

### Step 2: Calculate the total jumps needed to reach near the top.
The total depth of the well is 80 m. To find out how many jumps it takes to reach just below the top of the well (79.2 m), we can use the net distance per jump:

\[ \text{Total jumps to reach 79.2 m} = \frac{79.2 \, \text{m}}{0.4 \, \text{m/jump}} = 198 \, \text{jumps} \]

### Step 3: Calculate the position after the last jump.
After 198 jumps, the frog has covered 79.2 m. On the next jump (the 199th jump), the frog will jump up 1.15 m:

\[ \text{Distance after 199 jumps} = 79.2 \, \text{m} + 1.15 \, \text{m} = 80.35 \, \text{m} \]

### Step 4: Determine if the frog is out of the well.
Since 80.35 m is greater than the depth of the well (80 m), the frog successfully jumps out of the well after the 199th jump.

### Conclusion:
The total number of jumps after which the frog would be out of the well is **199 jumps**.

---