A and B together take 12 days less than A alone and 3 days less than B alone to complete the work. In how many days B alone complete the whole work? A और B मिलकर एक कार्य को पूरा करने में अकेले । से 12 दिन कम एवं B से 3 दिन कम लेते हैं। उसी कार्य को B अकेले कितने दिन में पूरा करता है?

Let A alone take x days and B alone take y days. Combined, they take (x-12) = (y-3) days. Work equation: 1/(x-12) = 1/x + 1/y. Substituting y = x-9: 1/(x-12) = 1/x + 1/(x-9). Solving gives (x-9)(x-12) = (x-12)(x-9) + x(x-9), which simplifies to x(x-9) - (x-9)(x-12) = 0. This gives (x-9)(x-x+12) = 0, so x = 9. Therefore y = 9 - 9 = 0, which is incorrect. Correct approach: 1/(x-12) - 1/x = 1/(x-9). This gives x/(x(x-12)) - (x-12)/(x(x-12)) = 1/(x-9), so 12/(x²-12x) = 1/(x-9). Cross-multiplying: 12(x-9) = x²-12x, giving x²-24x+108 = 0, so (x-6)(x-18) = 0. Since A takes more than 12 days, x = 18. Then y = 18-9 = 9 days.