a ball thrown upwards reaches point P of its path at the end of 4 seconds and the highest point Q at the end of 12 seconds. After how many seconds from the start will it reach point P again

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Solution

The ball reaches the point P in time 4 s. It reaches the highest point Q in 12 s.
Therefore, the time taken to cover distance between point P and Q is 8 s.
The ball will take the same time to cover the distance between Q and P when falling down as in both cases the acceleration is due to gravity.
Therefore, the ball reaches point P from point Q in time 8 s.
Therefore total time taken to reach the point P once again = 12 + 8 = 20 s

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