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Question

If the present ages of A and B are in the ratio 9 : 4 and seven years hence, the ratio of their ages will be 5 : 3, then find the their present ages.

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Solution

Let the present ages of A and B be a and b
ab=94
a=9b4
After 7 yrs ages of A and B will be a+7 & b+7
a+7b+7=53
3(a+7)=5(b+7)
3a+21=5b+35
3a=5b+14
3(9b4)=5b+14
27b45b=14
7b4=14
b=2×4=8
a=9×84=9×2=18
Present ages of A and B will be 18 and 8

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