Question:
The angular separation between the minute hand and the hour hand of clock 40 minutes passed after \(12 \mathrm{p} . \mathrm{m}\). is
The angular separation between the minute hand and the hour hand of clock 40 minutes passed after \(12 \mathrm{p} . \mathrm{m}\). is
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Minute hand moves 6 degrees per minute and hour hand moves 0.5 degree per minute.
Updated On: Nov 13, 2026
\(120^{\circ}\)
\(110^{\circ}\)
\(90^{\circ}\)
\(220^{\circ}\)
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The Correct Option is D
Solution and Explanation
Step 1: Understanding the Concept
Minute hand turns \(360^{\circ}\) in 60 min, i.e. \(6^{\circ}\) per minute. Hour hand turns \(360^{\circ}\) in 720 min, i.e. \(0.5^{\circ}\) per minute.
Step 2: After 40 Minutes
Minute hand: \(40\times 6 = 240^{\circ}\)
Hour hand: \(40\times 0.5 = 20^{\circ}\) (both measured from the 12 mark)
Step 3: Separation
\(240^{\circ} - 20^{\circ} = 220^{\circ}\), option D.
Final Answer:
The angular separation is 220 degrees. \[ \boxed{\text{(D) }220^{\circ}} \]
Minute hand turns \(360^{\circ}\) in 60 min, i.e. \(6^{\circ}\) per minute. Hour hand turns \(360^{\circ}\) in 720 min, i.e. \(0.5^{\circ}\) per minute.
Step 2: After 40 Minutes
Minute hand: \(40\times 6 = 240^{\circ}\)
Hour hand: \(40\times 0.5 = 20^{\circ}\) (both measured from the 12 mark)
Step 3: Separation
\(240^{\circ} - 20^{\circ} = 220^{\circ}\), option D.
Final Answer:
The angular separation is 220 degrees. \[ \boxed{\text{(D) }220^{\circ}} \]
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