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Explanation:
Let the required ratio of time be t1:t2:t3
Then using
Ratio of investments = ratio of proportions
4t1:6t2:9t3=2:3:5
Taking two first terms of the ratio,
4t1\6t2 = 2\3=>t1\t2=1\1=9\9
= > t1:t2=9:9
Taking last two terms of the ratio,
6t2\9t3 = 3\5 = t2\t3 = 9\10
= > t2:t3=9:10
So t1:t2:t3=9:9:10