A frog walking in a narrow lane takes `5` leaps forward and `3` leaps backward, then again `5` leaps forward and `3` leaps backward, and so on. Each leap is `1 m` long and requires `1 s`. Determine how long the frog takes to fall in a pit `13 m` away from the starting point.

Options

A. 35 s
B. 36 s
C. 37 s
D. 38 s

Explanation

To determine how long the frog takes to fall into a pit that is 13 m away from the starting point, we can analyze the frog's movement step by step.

### Step 1: Understand the frog's movement pattern
The frog takes 5 leaps forward and then 3 leaps backward. Each leap is 1 meter long and takes 1 second.

### Step 2: Calculate the net distance covered in one complete cycle
In one complete cycle:
- The frog moves forward 5 meters.
- Then, it moves backward 3 meters.

Net distance covered in one cycle = Distance forward - Distance backward
= 5 m - 3 m = 2 m.

### Step 3: Determine the time taken for one complete cycle
The time taken for one cycle consists of:
- Time for 5 leaps forward = 5 leaps × 1 second/leap = 5 seconds.
- Time for 3 leaps backward = 3 leaps × 1 second/leap = 3 seconds.

Total time for one cycle = Time forward + Time backward
= 5 seconds + 3 seconds = 8 seconds.

### Step 4: Calculate how many cycles are needed to reach or exceed 13 m
To find out how many complete cycles the frog needs to reach or exceed 13 m, we divide the total distance by the net distance covered in one cycle.

Number of complete cycles = Total distance / Net distance per cycle
= 13 m / 2 m = 6.5 cycles.

Since the frog cannot complete half a cycle, we will consider 6 complete cycles first.

### Step 5: Calculate the distance covered in 6 complete cycles
Distance covered in 6 complete cycles = Number of cycles × Net distance per cycle
= 6 cycles × 2 m/cycle = 12 m.

### Step 6: Calculate the time taken for 6 complete cycles
Time taken for 6 complete cycles = Number of cycles × Time per cycle
= 6 cycles × 8 seconds/cycle = 48 seconds.

### Step 7: Determine the remaining distance to the pit
After 6 complete cycles, the frog is at a distance of 12 m from the starting point. The pit is at 13 m, so the remaining distance to the pit is:
Remaining distance = 13 m - 12 m = 1 m.

### Step 8: Calculate the time taken to cover the remaining distance
To cover the remaining distance of 1 m, the frog will take 1 leap forward, which takes 1 second.

### Step 9: Calculate the total time taken to reach the pit
Total time taken = Time for 6 complete cycles + Time for the last leap
= 48 seconds + 1 second = 49 seconds.

### Final Answer
The frog takes a total of **49 seconds** to fall into the pit that is 13 m away from the starting point.

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