A girl saw a clock when it was 3 am. The clock loses 16 minutes per day. What will be the actual time when she sees the clock on the 4th day at 8 pm?

Options

A. `9:15` pm
B. `9:00` pm
C. `8:30` pm
D. `9:30` pm

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the problem
The girl sees the clock at 3 AM on the first day. The clock loses 16 minutes each day. We need to find out the actual time when she checks the clock on the 4th day at 8 PM.

### Step 2: Calculate the total time observed on the clock
The girl observes the clock from 3 AM on the first day to 8 PM on the 4th day. We need to calculate the total hours from this period.

- From 3 AM on Day 1 to 3 AM on Day 4 is 3 days, which is:
\[ 3 \text{ days} \times 24 \text{ hours/day} = 72 \text{ hours} \]
- From 3 AM on Day 4 to 8 PM on Day 4 is:
\[ 8 \text{ PM} - 3 \text{ AM} = 17 \text{ hours} \]
- Therefore, the total time observed on the clock is:
\[ 72 \text{ hours} + 17 \text{ hours} = 89 \text{ hours} \]

### Step 3: Calculate the total time lost by the clock
The clock loses 16 minutes per day. Over 4 days, the total loss is:
\[ 16 \text{ minutes/day} \times 4 \text{ days} = 64 \text{ minutes} \]

### Step 4: Convert the lost time into hours
To convert 64 minutes into hours:
\[ 64 \text{ minutes} = \frac{64}{60} \text{ hours} = 1.0667 \text{ hours} \approx 1 \text{ hour and } 4 \text{ minutes} \]

### Step 5: Calculate the actual time
The girl sees the clock showing 8 PM on the 4th day. Since the clock is slow, we need to add the lost time to find the actual time:
\[ 8 \text{ PM} + 1 \text{ hour and } 4 \text{ minutes} = 9 \text{ PM} + 4 \text{ minutes} \]
Thus, the actual time is approximately:
\[ 9:04 \text{ PM} \]

### Conclusion
The actual time when she checks the clock on the 4th day at 8 PM is approximately 9:04 PM.

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