Question

The minor angle between hours hand and minutes hand of a clock was observed at 8:48 am. The minimum deviation (in min) after 8:48 am on when angle increased by 50% is?

• A. \(\frac{24}{11}\)
• B. 4
• C. \(\frac{36}{11}\)
• D. 2

Answer 1

The Correct Option is A

The Correct answer is \(\frac{24}{11}\)

Answer 2

The hour hand completes one full rotation in \(12\) hours, rotating in the clockwise direction.
\(08:48\) is the time elapsed after \( 8.8\) hours(and not\( 8.48\) hours) from \(12\)-o-clock.
This means the angle covered by the hour hand is \(8.8 × 360 = 264°\)
At \(8:48\), the minutes' hand would have covered \(48 × 360 = 288° \)
 The difference is \(24\) degrees. Since the minutes' hand is ahead of the hours' hand at\( 8:48\),
 We need a further separation of \(12\) degrees.
Every minute the separation between them increases by\( ( 1/60 - 1/720)\times360\) degrees.
Therefore the time in minutes to achieve a difference of \(12\) degrees is, \( \frac{12}{\frac{11}{2}}\) =\(\frac{24}{11}\)