A clock gains 15 minutes per day. It is set right at 12 noon. What time will it show at 4.00 am, the next day?

Options

A. `4:10 AM`
B. `4:45 AM`
C. `4:20 AM`
D. `5:00 AM`

Answer

To solve the problem step-by-step, we will follow the reasoning provided in the video transcript:

### Step 1: Understand the problem
The clock gains 15 minutes every day. It is set correctly at 12 noon. We need to find out what time the clock will show at 4:00 AM the next day.

### Step 2: Calculate the time interval
From 12 noon to 4:00 AM the next day, we need to calculate the total hours:
- From 12 noon to midnight (12 AM) is 12 hours.
- From midnight to 4:00 AM is an additional 4 hours.
- Therefore, the total time from 12 noon to 4:00 AM is:
\[ 12 \text{ hours} + 4 \text{ hours} = 16 \text{ hours} \]

### Step 3: Determine the clock's gain in 16 hours
The clock gains 15 minutes in 24 hours. To find out how much it gains in 16 hours, we can use the unitary method:
- First, find the gain per hour:
\[ \text{Gain per hour} = \frac{15 \text{ minutes}}{24 \text{ hours}} = \frac{15}{24} \text{ minutes/hour} = \frac{5}{8} \text{ minutes/hour} \]
- Now, calculate the gain in 16 hours:
\[ \text{Gain in 16 hours} = \frac{5}{8} \text{ minutes/hour} \times 16 \text{ hours} = 10 \text{ minutes} \]

### Step 4: Calculate the time shown on the clock
At 4:00 AM, the clock will show the actual time plus the gain:
- Actual time = 4:00 AM
- Gain = 10 minutes
- Therefore, the time shown on the clock will be:
\[ 4:00 \text{ AM} + 10 \text{ minutes} = 4:10 \text{ AM} \]

### Final Answer
The clock will show **4:10 AM** at 4:00 AM the next day.

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