Question

Between 2 o'clock and 3 o'clock, at what time will the hands of a clock coincide?

• A. 15 minutes before 3
• B. \(2:20\)
• C. \(2:\dfrac{10}{11}\) minutes
• D. \(10\dfrac{1}{11}\) minutes before 3

Hint:

Clock problems become easy if you remember: \[ \text{Coincidence time} = \frac{60H}{11} \] where \(H\) is the hour number.

Answer 1

The Correct Option is D

Concept: The minute hand gains over the hour hand continuously. The formula for coincidence of hands between \(H\) and \(H+1\) hours is: \[ \text{Minutes} = \frac{60H}{11} \]

Step 1: Identify the hour interval. The clock hands coincide between: \[ 2 \text{ and } 3 \] Thus, \[ H = 2 \]

Step 2: Apply the formula. \[ \text{Minutes} = \frac{60 \times 2}{11} \] \[ = \frac{120}{11} \] \[ = 10\dfrac{10}{11}\text{ minutes} \] Therefore, the hands coincide at: \[ 2:10\dfrac{10}{11} \]

Step 3: Convert into the required option form. Time remaining for 3 o'clock: \[ 60 - 10\dfrac{10}{11} \] \[ = 49\dfrac{1}{11}\text{ minutes} \] Thus, the coincidence occurs: \[ 10\dfrac{1}{11}\text{ minutes before 3} \] Hence, \[ \boxed{10\dfrac{1}{11}\text{ minutes before 3}} \]