Question

Between 4 pm and 5 pm, if the hour hand and minute hand of a clock coincide after \(\frac{p}{q}\) minutes, then \(p+q=\)

• A. \(236\)
• B. \(280\)
• C. \(251\)
• D. \(261\)

Hint:

For coincidence of clock hands between \(H\) and \(H+1\), directly use \(\frac{60H}{11}\).

Answer 1

The Correct Option is C

Concept: The hands of a clock coincide every: \[ \frac{60H}{11} \] minutes after \(H\) o’clock. Formula: \[ \text{Time after }H=\frac{60H}{11} \] where \(H\) is the hour.

Step 1: Take \(H=4\).
Since the time is between: \[ 4 \text{ pm and } 5 \text{ pm} \] So: \[ \text{Coincidence time}=\frac{60 \times 4}{11} \] \[ =\frac{240}{11} \] minutes.

Step 2: Identify \(p\) and \(q\).
\[ p=240 \] \[ q=11 \]

Step 3: Find \(p+q\).
\[ 240+11=251 \] Thus, the required answer is: \[ \boxed{251} \]