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### Math Logic Problem

Math Logic Time Problem - 1 February

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 ?

1. How is it 200?

2. to arrive at the answer you must calculate the angle between the hands of the clock during that time. Using the longer hand as reference and rotating counter clockwise going to the shorter hand.

at 9:20 pm the longer hand points to number 4 while the shorter hand points somewhere between 9 & 10. to calculate the angle of the shorter hand in reference to 9 you must do this:

angle from 9 to shorter hand = (20/60) * 30 = 10 degrees

The angle between each number (from 9 to 10) is 30 degrees this means that the shorter hand is 20 degree far from the number 10

now from number 10 to number 4 (which the longer hand is pointing) we have 30 * (6) degrees which would give us 180 degrees

now to calculate for the total angle you should add 180 + 20 = 200

so the answer is 200 :)

3. I came up with 392. How can he hang painting number 200 when he has already hung painting number 315? Between 11am until 4pm, he hung 210 paintings (240 - 30), therefore he hung 210 paintings in 300 mins, which is equal to 7 paintings every 10 mins. Since there are 110 mins between 7:30pm and 9:20pm, he would have hung an additional 77 paintings in this time (after hanging number 315). Therefore, the answer is 315 + 77 = 392.

4. So 12 hours = 360 degrees right?
So 1 minute = 0.5 degrees.
Now the distance from the minute hand to hour hand = 5*60 + 20 minutes = 320 minutes.
So, the angle made by the hour hand and the minute hand in the clockwise direction (as is the pattern in the problem) = 360 - 320*0.5 degrees (320*0.5 because 320 minutes distance = 320*0.5 degrees) = 200.
So there you go, the answer to the problem is 200. Have a good day :)