Between 6 pm and 7 pm, the minute hand of a clock will be ahead of the hour hand by 3 minutes at:

6:36 pm

The correct answer is Option (3) → 6:36 pm

Step 1: Positions of hour and minute hands

• At 6:00, the hour hand is at 180° (6 × 30°), and the minute hand is at 0°.
• Let the time after 6:00 = t minutes.

Hour hand moves = $0.5° \text{ per minute}$ → angle = $180 + 0.5t°$
Minute hand moves = $6° \text{ per minute}$ → angle = 6t°

We want minute hand ahead by 3 minutes:

• 1 minute on a clock = 6°
• So 3 minutes = 18°

Step 2: Set up equation

$\text{Minute hand angle} - \text{Hour hand angle} = 18°$

$6t - (180 + 0.5t) = 18$

$6t - 180 - 0.5t = 18$

$5.5t = 198$

$t = \frac{198}{5.5} = 36\ \text{minutes}$

Step 3: Time

$6:00 + 36\ \text{minutes} = 6:36\ \text{pm}$