Question
Seven years ago from now, the ratio of ages of Om and
Jai was 3:4, respectively. Six years hence from now, the ratio of ages of Veer and Jai will be 4:5, respectively. If Veer is 2 years younger than Om, then find the age of Om, 'a' years hence from now, where 'a' is the smallest two-digit prime number.Solution
Let the ages of Om and Jai 7 years ago be 3x years and 4x years, respectively. Age of Veer 7 years ago = 3x−2 years Age of Om now = 3x+7 Age of Jai now = 4x+7 Six years hence: Age of Om = 3x+7+6=3x+13 Age of Jai = 4x+7+6=4x+13 Age of Veer = 3x+13−2=3x+11 Given: 
Solving the equation: 5×(3x+11)=4×(4x+13) 15x+55=16x+52 16x−15x=55−52 x=3 Since 11 is the smallest two-digit prime number: Age of Om, 11 years hence = 3x+7+11=3×3+7+11=27 years.
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