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CDS 2026 · PYQ · Time and Work / Variations · medium

12 men working 8 hours a day can completely build a wall of length 100 m, breadth 20 cm and height 5 m in 10 days. How many days will 16 men working 10 hours a day require to build a wall of length 200 m, breadth 60 cm and height 5 m?

  1. A.18✓ Correct
  2. B.24
  3. C.27
  4. D.36

Explanation

Using work formula: (M₁ × H₁ × D₁)/W₁ = (M₂ × H₂ × D₂)/W₂. Volume₁ = 100 × 0.2 × 5 = 100 m³. Volume₂ = 200 × 0.6 × 5 = 600 m³. So (12 × 8 × 10)/100 = (16 × 10 × D)/600. Thus 960/100 = 160D/600, giving 9.6 = 160D/600, so D = 9.6 × 600/160 = 5760/160 = 36. Hmm, let me recompute: 9.6 = D × 160/600 = D × 4/15. So D = 9.6 × 15/4 = 144/4 = 36. Answer: 36 days.
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