PUZZLE 37

1. The sum of three numbers is 272. If the ratio of first to second is 2 : 3 and that of second to third is 5 : 3, then find the first number?

1. Answer:80

Solution:If a,b,c are the required numbers then a : b = 2 : 3 and b : c = 5 : 3. Thus a : b : c = 10 : 15 : 9. Let a = 10k, b = 15k and c = 9k for some integer k. Then their sum = 34k which is given to be 272. Thus 34k = 272 and so k = 8. The first number = 10k = 80.

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