A and B together can complete a certain work in 20 days whereas B and C together can complete it in 24 days. If A is twice as good a workman as C, then in what time will B alone do 40% of the same work?

Let A, B, C be work rates (work per day). A + B = 1/20 and B + C = 1/24. Given A = 2C. Substituting: 2C + B = 1/20 and B + C = 1/24. Subtracting: C = 1/20 - 1/24 = (6-5)/120 = 1/80. So A = 2/80 = 1/40 and B = 1/24 - 1/80 = (10-3)/240 = 7/240. Wait, let me verify: from B + 1/80 = 1/24, B = 1/24 - 1/80 = (10-3)/240 = 7/240. For 40% work: B needs 0.40/(7/240) = 96/7 days. Hmm, let me recheck the calculation. Actually, from the given: A + B = 1/20 and A = 2C, so 2C + B = 1/20. Also B + C = 1/24. From these, C = 1/20 - 1/24 + C... wait. Subtracting: (2C + B) - (B + C) = 1/20 - 1/24, so C = 1/120. Then A = 1/60, and B = 1/24 - 1/120 = 4/120 = 1/30. For 40% work by B alone: 0.40/(1/30) = 12 days.