Question
Ratio of present age of 'A' to that of 'B' is 4:7. If
the age of 'B' three years hence from now will be 31 years, then after how many years, the ratio of the age of 'B' to that of 'A' will become 5:4?Solution
Let the present ages of 'A' and 'B' be '4m' and '7m' years respectively.
So, 7m + 3 = 31
Or, 7m = 28
So, 'm' = 4
Present age of 'A' = 4m = 16 years
Present age of 'B' = 7m = 28 years
Let ratio of the ages of 'B' to 'A' becomes 5:4 after 'n' years.
So, (16 + n) : (28 + n) = 4 : 5
Or, 5 Ă— (16 + n) = 4 Ă— (28 + n)
Or, 80 + 5n = 112 + 4n
So, 'n' = 32
Hence, option D.
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