Question
Four years ago, the ratio of ages of ‘Ravi’ and his
sister was 3:4, respectively. 4 years from now, the ratio of ages of Ravi and his mother will be 2:5. 10 years from now, the ratio of ages of Ravi’s sister and his mother will be 3:5. What is the present age of Ravi’s mother?Solution
ATQ,
4 years ago, let the age of Ravi = 3x years So, age of Ravi’s sister = (4/3) × 3x = 4x years 4 years hence from now, age of Ravi = (3x + 8) years So, age of Ravi’s mother = (3x + 8) × (5/2) = (15x + 40)/2 = 7.5x + 20 10 years hence from now: Ravi’s sister = 4x + 14 Ravi’s mother = (7.5x + 20) + 6 = 7.5x + 30 ATQ: 4x + 14 = (3/5) × (7.5x + 30) ⇒ 5(4x + 14) = 3(7.5x + 30) ⇒ 20x + 70 = 22.5x + 90 ⇒ 2.5x = 20 ⇒ x = 8 So, present age of Ravi’s mother = 7.5x + 20 – 4 = 7.5 × 8 + 16 = 60 + 16 = 76 years
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