Lock of a safe consists of five discs each of which features the digits 0, 1, 2, ….., 9. The safe can be opened by dialing a special combination of the digits. If the work day lasts 13 hours and to dial one combination of digits takes 5 seconds, then number of days sufficient enough to open the safe, are

Options

A. 9
B. 10
C. 11
D. 12

Answer

To solve the problem, we need to determine how many days it would take to try all possible combinations for the lock of the safe. Let's break it down step by step.

### Step 1: Calculate the total number of combinations
The lock consists of 5 discs, and each disc can feature any digit from 0 to 9. Therefore, each disc has 10 possible digits.

The total number of combinations can be calculated as:
\[ \text{Total combinations} = 10^5 \]
Calculating this gives:
\[ 10^5 = 100000 \]

### Step 2: Calculate the total time to try all combinations
It takes 5 seconds to dial one combination. Therefore, the total time required to try all combinations is:
\[ \text{Total time (in seconds)} = \text{Total combinations} \times \text{Time per combination} \]
Substituting the values we have:
\[ \text{Total time} = 100000 \times 5 = 500000 \text{ seconds} \]

### Step 3: Convert total time from seconds to hours
To convert seconds into hours, we divide by the number of seconds in an hour (3600 seconds):
\[ \text{Total time (in hours)} = \frac{500000}{3600} \]
Calculating this gives:
\[ \text{Total time (in hours)} \approx 138.89 \text{ hours} \]

### Step 4: Calculate the number of workdays required
Given that a workday lasts 13 hours, we can find the number of workdays required by dividing the total hours by the number of hours in a workday:
\[ \text{Number of days} = \frac{\text{Total time (in hours)}}{\text{Hours per workday}} = \frac{138.89}{13} \]
Calculating this gives:
\[ \text{Number of days} \approx 10.69 \]

### Step 5: Round up to the nearest whole number
Since we cannot have a fraction of a day, we round up to the nearest whole number:
\[ \text{Number of days required} = 11 \]

Thus, the number of days sufficient enough to open the safe is **11 days**.