Discussion

Ramesh wants to set the clock hands 8 minutes apart between 10 o'clock and 11 o'clock. What would be the time shown in the clock if he does so?

A.3(3/11) minutes before 11 o’ clock and 63(3/11) minutes past 10 o’ clock
B.\( 45\tfrac{9}{11} \) minutes past 10 o’ clock and \( 3\tfrac{3}{11} \) minutes past 11 o’ clock
C.43(9/11) minutes past 10 o’ clock and 58(9/11) minutes before 11 o’ clock
D.43(8/11) minutes past 10 o’ clock and 3(3/11) minutes before 11 o’ clock

Answer: B

The hour hand moves \( 0.5^{\circ} \) a minute and the minute hand \( 6^{\circ} \), so at \( H \) hours \( M \) minutes the angle between them is

\[ \theta = \left| 30H - 5.5M \right| \]

Eight minute-divisions is \( 8 \times 6 = 48^{\circ} \), so with \( H = 10 \):

\[ \left| 300 - 5.5M \right| = 48 \]

\[ 5.5M = 252 \quad\Longrightarrow\quad M = \frac{504}{11} = 45\tfrac{9}{11} \]

\[ 5.5M = 348 \quad\Longrightarrow\quad M = \frac{696}{11} = 63\tfrac{3}{11} \]

The second value exceeds 60, so it falls in the next hour: \( 3\tfrac{3}{11} \) minutes past 11.

The hands coincide at \( 54\tfrac{6}{11} \) minutes past 10, and the two answers sit on either side of that moment.

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