Question
Nine years ago, the ratio of ages of Raj and Vijay was
5:7, respectively. Four years hence, the ratio of ages of Sanjay and Vijay will be 2:3, respectively. If Sanjay is 2 years younger than Raj, find the age of Raj, 'e' years hence from now, where 'e' is the fifth smallest two-digit prime number.Solution
ATQ Let the ages of Raj and Vijay 9 years ago be '5p' years and '7p' years, respectively. So, age of Sanjay 9 years ago = (5p - 2) years. ATQ, 
3 × (5p + 11) = 2 × (7p + 13) 15p + 33 = 14p + 26 14p - 15p = 26 - 33 p = 7 Since, 23 is the fifth smallest two-digit prime number. So, 'e' = 23 Therefore, age of Raj, 23 years hence = 5p + 9 + 23 = 5 × 7 + 32 = 35 + 32 = 67 years
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