At what time between 8 and 9 o'clock will the hands of a watch be in straight line but not together ?

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$12 \frac{10}{11} \min$ . past 8

$11 \frac{10}{11} \min$ . past 8

$10 \frac{10}{11} \min$ . past 8

$10 \frac{11}{10} \min .$ past 8

answer is B.

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Detailed Solution

At 8 o'clock, the hands of the watch are 20 min. spaces apart.

To be in straight line but not together they will be 30 min. space apart.

$∴$ Minute hand will have to gain 10 min. spaces

55 min. spaces are gained in 60 min.

10 min. spaces will be gained in

$(\frac{60}{55} \times 50) \min$ or $10 \frac{10}{11} \min$

$∴$ Required time $= 10 \frac{10}{11} \min .$ past 8

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