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1. At 3:40, the hour hand and the minute hand of a clock form an angle of:

A. 120°

B. 125°

C. 130°

D. 135°

Solution:

\begin{aligned} Angle traced by hour hand in 12 hrs = 36 0^{\circ} \\ Angle traced by it in \frac{11}{3} hrs \\ = {(\frac{360}{12} \times \frac{11}{3})}^{\circ} = 110^{\circ} \\ Angle traced by min . hand in 60 min = 36 0^{\circ} \\ Angle traced by it in 40 min . \\ = {(\frac{360}{60} \times 40)}^{\circ} = 240^{\circ} \\ ∴ Required angle \\ = {(240 - 110)}^{\circ} = 130^{\circ} \end{aligned}

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