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?
\(\frac{24}{11}\)
4
\(\frac{36}{11}\)
2
The Correct Option is A
Approach Solution - 1
The Correct answer is \(\frac{24}{11}\)
Approach Solution -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, \( \frac{12}{\frac{11}{2}}\) =\(\frac{24}{11}\)
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