In billiards, Nikhil can give Om 24 points in a game of 120, and Om can give Prakash 30 points in a game of 150. How many points can Nikhil give Prakash in a game of 200?

Om scores 96 while Nikhil scores 120: rate 0.8. Prakash scores 120 while Om scores 150: rate 0.8. So Prakash's rate is $0.8\times 0.8=0.64$ of Nikhil's; in a game of 200 he scores 128, so Nikhil gives $200-128=72$. (54 just adds 24 and 30.)