At what time, in minutes, between 3 oclock and 4 oclock, both the needles will coincide each other? Options: A . &nbsp \(5\frac{1}{11}\) B . &nbsp \(12\frac{4}{11}\) C . &nbsp \(13\frac{4}{11}\) D . &nbsp \(16\frac{4}{11}\)

At what time, in minutes, between 3 oclock and 4 oclock, both the needles will c

Question

At what time, in minutes, between 3 oclock and 4 oclock, both the needles will coincide each other?

Options:

A . \(5\frac{1}{11}\)

B . \(12\frac{4}{11}\)

C . \(13\frac{4}{11}\)

D . \(16\frac{4}{11}\)

Answer: Option D

At 3 o'clock, the minute hand is 15 min. spaces apart from the hour hand.

To be coincident, it must gain 15 min. spaces.

55 min. are gained in 60 min.

15 min. are gained in \(\left(\frac{60}{55}\times15\right)min. = 16\frac{4}{11}min.\)

So, The hands are coincident at \(16\frac{4}{11}min. past 3\)

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