If the angle between 2 hands of a clock is 35 degrees and the hour hand is between 3 and 4, what time does the clock show?

The hour hand covers 30 degrees in 1 hour or 0.5 degrees / min

The min hand covers 360 degrees in 1 hour of 6 degrees/ min

Hence, we can say that the the minute hand gains 6 - 0.5 = 5.5 degrees on hour hand, every minute. 

At 3 p.m. the angle between the hands was 90 degrees

Hence there can be two possible cases, the minute hand can form a angle of 35 degrees both before and after the it crosses the hour hand. 

Let x be the number of minutes past 3. 

case 1 

90 - 5.5x = 35 

x = 10 

case 2

5.5x - 90 = 35 

x = 125/5.5 = 250/11 = 22 8/11

Hence the angle between hour hand and minute hand will be 35 degrees at 10 and 22 8/11 minutes past 3