A clock hung on a wall has marks instead of numerals in its dial. On the adjoining wall, there is a plane mirror and the image of the clock in the mirror indicates the time `4.20`. Then the time on the clock is

Options

A. `7.40`
B. `4.20`
C. `2.40`
D. `4.07`

Explanation

To determine the actual time on the clock when the mirror shows the time as 4:20, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We have a clock showing a time of 4:20 in the mirror. We need to find out what time it actually is on the clock.

2. **Visualize the Clock**: Draw a simple clock face. Mark the positions of the hour and minute hands at 4:20. The minute hand will be on the 4 (indicating 20 minutes past the hour), and the hour hand will be slightly past the 4.

3. **Mirror Reflection**: When you look at the clock in the mirror, the positions of the hands will appear reversed. The minute hand at 20 minutes will appear at 40 minutes on the clock face (since 60 - 20 = 40). The hour hand will also be reflected.

4. **Calculate the Actual Time**: To find the actual time on the clock, we can use the formula:
\[ \text{Actual Time} = 12:00 - \text{Mirror Time} \]
Here, the mirror time is 4:20.

5. **Perform the Calculation**:
- Convert 4:20 into a 12-hour format:
- 4:20 in the mirror means the hour hand is between 4 and 5, and the minute hand is at 4 (20 minutes).
- Now, apply the formula:
\[ \text{Actual Time} = 12:00 - 4:20 \]
- To subtract, we can convert 4:20 into minutes:
- 4 hours = 240 minutes
- 20 minutes = 20 minutes
- Total = 240 + 20 = 260 minutes
- Now, convert 12:00 into minutes:
- 12 hours = 720 minutes
- Now perform the subtraction:
\[ 720 - 260 = 460 \text{ minutes} \]
- Convert 460 minutes back into hours and minutes:
- 460 minutes = 7 hours and 40 minutes (since 7 hours = 420 minutes and 40 minutes = 40 minutes)
- Therefore, the actual time on the clock is:
\[ 7:40 \]

### Final Answer:
The time on the clock is **7:40**.

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