If measured in radians is the angle between the hour hand and the minute hand of a clock when the ti...........

Quantitative Aptitude (CDS) Coordinate Geometry

If ?? measured in radians is the angle between the hour hand and the minute hand of a clock when the time is 4 : 36 pm, then which one of the following is correct?

$\frac{3\pi}{5}< \Theta < \frac{4\pi}{5}$

$\frac{2\pi}{5}< \Theta < \frac{3\pi}{5}$

$\frac{\pi}{5}\leq \Theta \leq \frac{2\pi}{5}$

$\frac{7\pi}{15}< \Theta < \frac{8\pi}{5}$

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Explanation:

For calculating the angle between the hour hand and the minute hand of a clock when the time is
4 : 36 pm, we can say that the angle will be approximately equal to the angle made from 4 :20 pm to 4 : 36 pm.
Thus, we need to calculate the angle made by the hands of a clock in 16 minutes.
In 60 minutes, the angle made by the hands of a clock is 360°.
So, the angle made by the hands of a clock in 16 minutes = 360/60×16=96⁰
Thus, the angle lies between 72° to 108° i.e. 2 $\pi$ /5 to 3 $\pi$ /5
Hence, $\frac{2\pi}{5}< \Theta < \frac{3\pi}{5}$