At what angle the hands of a clock are inclined at 15 minutes past 5? Options: A . &nbsp \(58\frac{1}{2}^{0}\) B . &nbsp64º C . &nbsp \(67\frac{1}{2}^{0}\) D . &nbsp \(72\frac{1}{2}^{0}\)

At what angle the hands of a clock are inclined at 15 minutes past 5?

Question

At what angle the hands of a clock are inclined at 15 minutes past 5?

Options:

A . \(58\frac{1}{2}^{0}\)

B . 64º

C . \(67\frac{1}{2}^{0}\)

D . \(72\frac{1}{2}^{0}\)

Answer: Option C

Angle traced by hour hand in \(\frac{21}{4}hrs = \left(\frac{360}{12}\times\frac{21}{4}\right)^{0}=157\frac{1}{2}^{0} \)

Angle traced by min. hand in 15 min. = \(\left(\frac{360}{60}\times15\right)^{0}=90^{0} \)

So, Required angle = \(\left(157\frac{1}{2}\right)^{0}-90^{0} =67\frac{1}{2}^{0}\)

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