The angle between the two hands of a clock is `30^(@)`, when the hour hand is between 5 and 6. What time does the watch show ?

Options

A. 5 hours `20""20/11` minutes
B. 5 hours `27""3/11` minutes
C. 5 hours `30""30/11`
D. Both (a) and (c)

Answer

D

Explanation

From the formula, `theta=11/2m-30h" [when "11/2m gt 30h]`
According to the question,

Here `theta=30^(@), h=5`.
So, `30=11/2m-30 times 5`
or, `m=(30 times 2+30 times 5 times 2)/11" or, "m=(60+300)/11=360/11`
or, `m=30""30/11` minutes past 5 o.clock.
Also, `theta=30h-11/2m" [when" 30h gt 11/2m]`
So, `30=30 times -11/2m or, m=(30 times 5 times 2-30 times 2)/11`

or, `m=(300-60)/11=240/11`
or, `m=20""20/11` minutes past 5 o.clock.
Therefore, the angle between the two hands is `30^(@)`.
when the clock shows = 5 hours `30""30/11` minutes and 5 hours `20""20/11` minutes.