Question
Three years ago, the ratio of ages of Rohit and Mohan
was 6:7, respectively. Five years hence, the ratio of ages of Soham and Mohan will be 3:4, respectively. If Soham is 5 years younger than Rohit, find the age of Rohit, 'f' years hence from now, where 'f' is the sixth smallest two-digit prime number.Solution
ATQ Let the ages of Rohit and Mohan 3 years ago be '6k' years and '7k' years, respectively. So, age of Soham 3 years ago = (6k - 5) years. ATQ, 
4 × (6k + 3) = 3 × (7k + 8) 24k + 12 = 21k + 24 24k - 21k = 24 - 12 k = 4 Since, 29 is the sixth smallest two-digit prime number. So, 'f' = 29 Therefore, age of Rohit, 29 years hence = 6k + 3 + 29 = 6 × 4 + 32 = 24 + 32 = 56 years
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