Find the time between 5 and 6 o'clock when the two hands of clock are 6 minutes spaces apart.

(a) 3 2/11 minutes past 5 o'clock
(b) 6 6/11 minutes past 5 o'clock
(c) 208/11 minutes past 5 o'clock
(d) 4 2/11 minutes past 5 o'clock

Hi,

1min-->6 deg
6min-->36 deg

5*30 = 150 deg....but both are 6 min apart it means 150-36=114 deg distance
T = d/s = 114/(11/2) = 228/11 = 20 8/11.

Answeris C

Well solve it in another way

Consider the clock, at 5 hours the minute hand is 25 minutes spaces behind the hour hand.
Here we will see two cases:

case 1 :- Minute hand is 6min spaces behind of the hour hand
In this case , the minute hand has to gain (25-6) = 19minute spaces
55 min spaces are gained in 60 min
19 min spaces are gained in [(19/55) * 60] = (20) 8/11 min.

case 2 :- Minute hand is 6min spaces ahead of the hour hand
In this case , the minute hand has to gain (25+6) = 31minute spaces
55 min spaces are gained in 60 min
31 min spaces are gained in [(31/55) * 60] = (33) 9/11 min.

Because in options case 2 is not mentioned so we consider option 3.

Hope the answer of your question !