Three years ago, the ratio of ages of ‘Ravi’ and his sister was 3:4. Three years from now, the ratio of ages of Ravi and his mother will be 2:5. In 9 years from now, the ratio of ages of Ravi’s sister and his mother will be 3:5. What is the current age of Ravi’s mother?

3 years ago, let the age of Ravi = 3x years So, 3 years ago, age of Ravi’s sister = (4/3) × 3x = 4x years 3 years hence from now, age of Ravi = (3x + 6) years 3 years hence from now, age of Ravi’s mother = (3x + 6) × (5/2) = (15x + 30)/2 years 9 years hence from now, age of Ravi’s sister = (4x + 12) years 9 years hence from now, age of Ravi’s mother = (15x + 30)/2 + 6 = (15x + 42)/2 years ATQ; 4x + 12 = (15x + 42)/2 × (3/5) Or, 4x + 12 = {(45x + 126)/10} Or, 40x + 120 = 45x + 126 Or, 5x = 6 Or, x = 6 So, present age of Ravi’s mother = (15x + 30)/2 – 3 = (90 + 30)/2 – 3 = 60 – 3 = 57 years