Question
2n years ago, the age of Rahul was four times that of
his son and n years ago, the age of Rahul was thrice that of his son. If n years later, the sum of the ages of Rahul and his son will be 80 years, then the difference in the ages of Rahul and his son is –Solution
Let the present ages of Rahul and his son be x and y respectively. 2n years ago, => x – 2n = 4(y – 2n) => x = 4y – 6n ------ (i) n years ago, => x - n = 3(y – n) => x = 3y – 2n ------ (ii) Solving (i) and (ii) we get, => y = 4n => x = 4 × 4n – 6n = 10n Now n years later, => x + n + y + n = 80 => 4n + n + 10n + n = 80 => 16n = 80 => n = 5 Required difference = 10n – 4n = 6n = 30 years
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