In a modern art gallery, an artist has numerous modern art paintings created by him. He hangs different painting on the space provided to him periodically. When the clock hit 11 am, he hung the painting number 30. When it struck 4 pm, he hung the painting number 240 and when it struck 7:30 pm, he hung painting number 315.

Can you determine, which painting number will he hang when the time is 9:20 pm ?

Math Logic Problem

He will hang painting number 200 at that time. Every time he hangs the painting, the number of it corresponds with the angle between the minute and hour hand of the clocks.