Solution

Combined ratio of efficiency of (A + B), (B + C) and (A + C) is: A + B B + C A + C 4 5 5 7 -------------------------------------------------- 4k : 5k : 7k (Where K is a constant) A + B + B + C + A + C = 2(A + B + C) and 2(A + B + C) = 16k A + B + C = 8 k Note that combined efficiency of (A + B + C) is twice of the efficiency of (A + B). [Since, 8 = 4 × 2] Therefore, A and B working together will finish the work in (40 × 8)/4 days (40 × (12-4))/4 days 40 $ (12 # 4) ^ 4 days Similarly, B and C working together will finish the work in (40 × 8)/5 days (40 × (4+4))/5 Days 40 $ (4 @ 4) ^ 5 days Similarly, A and C working together will finish the work in (40 × 8)/7days (40 × (12-4))/7 Days 40 $ (12 @ 4) ^ 7 days Again, time required to finish the work by A alone (64 ×40)/ (64-40) Days 64 $ 40 ^ (64 # 40) days Since, B and C working together finish the work in 64 days while A, B and C working together finish the work in 40 days.