Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is 1/6. Find their present ages.

Vivek is older than Kishor by 5 years. The sum of the reciprocals of their ages is \(\frac{1}{6}\). Find their present ages.

Doubtly Asked 24 Oct 2026 Save WhatsApp Report

1 answer

Answer: Kishor is 10 years old and Vivek is 15 years old.

Let Kishor's age be \(x\) years; Vivek's age \(= x + 5\).

\[\frac{1}{x} + \frac{1}{x + 5} = \frac{1}{6}\]\[6(2x + 5) = x(x + 5)\]\[x^2 - 7x - 30 = 0\]\[(x - 10)(x + 3) = 0\]

\(x = 10\). Check: \(\frac{1}{10} + \frac{1}{15} = \frac{3 + 2}{30} = \frac{1}{6}\).

Doubtly AI · 24 Oct 2026 AI-verified · Oct 2026 Report

Was this answer helpful?