Question
Eight years ago, the ratio of the ages of Rohan and
Sohan was 5:6, respectively. Five years hence, the ratio of the ages of Mohan and Sohan will be 6:7, respectively. If Mohan is 3 years younger than Rohan, find the age of Rohan, 'a' years hence, where 'a' is the smallest two-digit composite number.Solution
ATQ, Let the ages of Rohan and Sohan 8 years ago be 5x years and 6x years, respectively. Age of Mohan 8 years ago = 5x−3 years Age of Rohan now = 5x+8 Age of Sohan now = 6x+8 Five years hence: Age of Rohan = 5x+8+5=5x+13 Age of Sohan = 6x+8+5=6x+13 Age of Mohan = 5x+13−3=5x+10 Given: 
Solving the equation: 7×(5x+10)=6×(6x+13) 35x+70=36x+78 36x−35x=70−78 x=8 Since 10 is the smallest two-digit composite number: Age of Rohan, 10 years hence = 5x+8+10=5×8+8+10=58 years.
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