A clock gains 2 minutes every hour. If it was set right at 6:00 AM, what will be the time shown at 6:00 PM on the clock?
- 6:20 PM
- 6:24 PM
- 6:12 PM
- 6:30 PM
The Correct Option is B
Solution and Explanation
Concept:
A clock gains 2 minutes every hour. Therefore, for every actual hour that passes, the clock advances \[ 60+2=62 \text{ minutes}. \] To find the time shown by the clock after a given period, first determine the total gain during that period.
Step 1: Calculate the actual elapsed time.
The clock is set correctly at \[ 6:00\ \text{AM}. \] We need to find the reading at \[ 6:00\ \text{PM}. \] The actual time elapsed is \[ 12 \text{ hours}. \]
Step 2: Calculate the total gain.
The clock gains \[ 2 \text{ minutes/hour}. \] In \(12\) hours, the gain is \[ 12 \times 2 = 24 \text{ minutes}. \]
Step 3: Find the clock reading.
At the actual time \[ 6:00\ \text{PM}, \] the clock will be ahead by \[ 24 \text{ minutes}. \] Hence, it will show \[ 6:00\ \text{PM} + 24 \text{ minutes} = 6:24\ \text{PM}. \]
Step 4: Match with the options.
\[ \begin{array}{|c|c|} \hline \text{Option} & \text{Time} \\ \hline (A) & 6:20\ \text{PM} \\ (B) & 6:24\ \text{PM} \\ (C) & 6:12\ \text{PM} \\ (D) & 6:30\ \text{PM} \\ \hline \end{array} \] Thus, the correct option is \[ \boxed{\text{(B)}}. \]
Final Answer: \[ \boxed{6:24\ \text{PM}} \]
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