Question
The present ages of P and Q are in the ratio 4 : 5. Eight years ago, the ratio of their ages was 2 : 3. The harmonic mean of their present ages is
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RRB NTPC 2025 Under Graduate CBT 1 Question Paper PDF (20-Jun-2026) (Shift 3)
The correct answer is
17\(\tfrac79\) years
Let P=4x, Q=5x. Eight years ago: \(\dfrac{4x-8}{5x-8} = \dfrac23\).
\(3(4x-8) = 2(5x-8) \Rightarrow 12x-24 = 10x-16 \Rightarrow 2x=8 \Rightarrow x=4\). So P=16, Q=20.
Harmonic mean: \(\dfrac{2PQ}{P+Q} = \dfrac{2\times16\times20}{36} = \dfrac{640}{36} = 17\tfrac{7}{9}\).
Hence, the harmonic mean of their present ages is \(17\tfrac79\) years.
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