Question
Eight years ago, the ratio of the ages of Ram and Shyam
was 5:6, respectively. Seven years hence, the ratio of the ages of Prem and Shyam will be 3:4, respectively. If Prem is 3 years younger than Ram, find the age of Ram, 'b' years hence from now, where 'b' is the second smallest two-digit prime number.Solution
ATQ Let the ages of Ram and Shyam 8 years ago be '5y' years and '6y' years, respectively. So, age of Prem 8 years ago = (5y - 3) years. ATQ, 
4 × (5y + 12) = 3 × (6y + 15) 20y + 48 = 18y + 45 20y - 18y = 45 - 48 y = 3 Since, 13 is the second smallest two-digit prime number. So, 'b' = 13 Therefore, age of Ram, 13 years hence = 5y + 8 + 13 = 5 × 3 + 21 = 36 years
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