Question

A locker in bank has 3 digit lock. Mahesh forgot his password and was trying all possible combinations. He took 6 seconds for each try. The problem was that each digit can be from 0 to 9. How much time will be needed by Mahesh to try all the combinations?

• A. \(90\) minutes
• B. \(120\) minutes
• C. \(60\) minutes
• D. \(100\) minutes

Hint:

If each digit has 10 choices and there are 3 digits, total codes are: \[ 10^3=1000 \]

Answer 1

The Correct Option is D

Concept:
This is a counting and time calculation problem. A 3-digit lock means there are three positions. Each position can contain any digit from: \[ 0 \text{ to } 9 \] So each position has: \[ 10 \] choices.

Step 1: Count possible combinations.
For the first digit: \[ 10 \] choices. For the second digit: \[ 10 \] choices. For the third digit: \[ 10 \] choices. Therefore, total combinations: \[ 10\times10\times10=1000 \]

Step 2: Calculate total time in seconds.
Time required for one try: \[ 6\text{ seconds} \] Total tries: \[ 1000 \] So total time: \[ 1000\times6=6000\text{ seconds} \]

Step 3: Convert seconds into minutes.
We know: \[ 1\text{ minute}=60\text{ seconds} \] So: \[ 6000\text{ seconds}=\frac{6000}{60}\text{ minutes} \] \[ =100\text{ minutes} \]

Step 4: Check the options.
Option (A) \(90\) minutes is incorrect.
Option (B) \(120\) minutes is incorrect.
Option (C) \(60\) minutes is incorrect.
Option (D) \(100\) minutes is correct. Hence, the correct answer is: \[ \boxed{(D)\ 100\text{ minutes}} \]