In a lake, there are 10 steps labelled using alphabets from A to J. Starting from step A, every minute a frog jumps to the 4th step from where it started - that is from the step A it would go to the step E and from E it would go to the step I and from I it would go to C etc. Where would the frog be at the 60th minute if it starts at the step A ?

Options

A. D
B. H
C. A
D. B

Answer

To solve the problem, we need to determine where the frog will be after 60 minutes, given that it jumps to the 4th step from its current position every minute. We will label the steps from A to J as follows:

- A = 0
- B = 1
- C = 2
- D = 3
- E = 4
- F = 5
- G = 6
- H = 7
- I = 8
- J = 9

Since the frog jumps to the 4th step from its current position, we can represent the movement mathematically. The frog's position after each jump can be calculated using modular arithmetic since there are 10 steps (0 to 9).

### Step-by-step Solution:

1. **Initial Position**: The frog starts at step A, which is position 0.

2. **Jump Calculation**: Every minute, the frog jumps 4 steps forward. Therefore, after \( n \) minutes, the position can be calculated as:
\[ \text{Position after } n \text{ minutes} = (0 + 4n) \mod 10 \]

3. **Calculate Position after 60 Minutes**:
\[ \text{Position after 60 minutes} = (0 + 4 \times 60) \mod 10 \]
\[ = (240) \mod 10 \]
\[ = 0 \]

4. **Determine the Step**: Since the position is 0, the frog is at step A.

### Conclusion:
After 60 minutes, the frog will be at step A.