Question
Six years ago, the ratio of ages of Alok and Ravi was
7:9, respectively. Eight years hence, the ratio of ages of Rohan and Ravi will be 5:6, respectively. If Rohan is 1 year younger than Alok, find the age of Alok, 'c' years hence from now, where 'c' is the third smallest two-digit prime number.Solution
ATQ Let the ages of Alok and Ravi 6 years ago be '7z' years and '9z' years, respectively. So, age of Rohan 6 years ago = (7z - 1) years. ATQ, 
6 × (7z + 13) = 5 × (9z + 14) 42z + 78 = 45z + 70 45z - 42z = 78 - 70 z = 8/3 Since, 17 is the third smallest two-digit prime number. So, 'c' = 17 Therefore, age of Alok, 17 years hence = 7z + 6 + 17 = 7 × (8/3) + 23 = 18 + 23 = 41 years
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