A bus for Delhi leaves every 30 minutes from a bus stand. An inquiry clerk told a passenger that the bus had already left 10 min ago and next bus will leave at 9 : 35 am. At what time did the inquiry clerk give this information to the passenger?

Total number of days from January 1 to march 1
     = 31 + 29 + 1
     = 61 days
(February in leap years = 29 days) = 61 ÷ 7
     = 8 weeks and 5 odd days
So, the fifth day from Friday = Tuesday

The century divisible by 400 is a leap year. The year 707 is not a leap year.

Everyday of the week is repeated after 7 days. Hence, after 56 days, it would be Thursday again and after 59 days, it would be Sunday.

Everyday of the weeks is repeated after 7 days.
Hence, it will be Wednesday after 84 days.

Each day of the week is repeated after 7 days.
So, after 63 days, it will be Monday.
After 61 days, it will be Saturday.

Three days after Saturday is Tuesday and Tuesday is a day before a day before yesterday So, yesterday is Tuesday.
Hence, today is Friday.

At 4 : 20 A.M. from the formula here P = 4 and Q = 20 so required angle is 11 x 20/2 - 30 x 4 = 110 - 120 = - 10 or ignoring the negative sign the required angle is 10°

At 1 : 40 from the formula here P = 1 and Q = 40 so required angle is 11 x 40/2 - 30 x 1 = 220 - 30 = 190 the required angle is 190°

At 10 : 10 from the formula here P = 10 and Q = 10 so required angle is 11 x 10/2 - 30 x 10 = 55 - 300 = - 245 the required angle is 245°

Consider exactly at 3 : 00, minute hand is at position '12' and hour hand is at '3' hence angle between these two hands at 3 : 00 is 90°.
Since relative speed between them is 11/2° per minute or every minute the minute hand will travel 11/2° more than the hour hand.
They will be together when the minute hand will travel 90° more than the hour hand. And time taken for this is (90)/(11/2) = 180/11 or 16 4/11 minute.
Hence they will coincide at 3 : 16 minute : 21.81 second