The ratio of Ahmed’s age to Mohammed’s age is the same as the ratio of the ages of their respective elder brothers. The ratio of the difference of the ages of Ahmed and Mohammed to that of the difference of the ages of their respective brothers is 1 : 2. What is the ratio of the sum of the ages of their respective brothers to the sum of the ages of Ahmed and Mohammed?
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1) Let the ages of Ahemed be 'a' years and that of Mohammed be 'b' years; and their respective elder brothers ages be c & d years.
2) So as given a/b = c/d
3) Then applying Compenendo & Dividendo property of Ratio/Proportions,
(a + b)/(a - b) = (c + d)/(c - d)
==> (a + b)/(c + d) = (a - b)/(c - d)
But given the ratio of differences, that is (a - b)/(c - d) = 1/2
Hence of the above, the ratio of sum of their ages (a + b)/(c + d) = 1/2
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