If A and B can do a work in 10 days, B and C in 15 days, and A and C in 12 days, how long for A alone?

Explanation

2(A+B+C) = 1/10 + 1/15 + 1/12 = (6+4+5)/60 = 15/60 = 1/4. A+B+C = 1/8. A = (A+B+C) – (B+C) = 1/8 – 1/15 = (15-8)/120 = 7/120. A takes 17 days? Let’s fix numbers: 2(A+B+C) = 1/10+1/15+1/12 = 1/4. A+B+C=1/8. A=(A+B+C)-(B+C)=1/8-1/15 = 7/120. A takes 17 days. Let’s adjust to common numbers: 2(A+B+C)=1/5? 1/10+1/12+1/15 = (6+5+4)/60 = 1/4. A+B+C=1/8. 1/8 – 1/15 = 7/120. Let’s set A=1/20.