Question
Which of the following equations represents the number
of days in which A and B Working together can finish the same work? In the following coded arithmetic questions certain symbols are used with the following meaning: I. P @ Q means add P to Q. II. P # Q means subtract Q from P. III. P $ Q means multiply P with Q. IV. P ^ Q means divide P by Q. Now study the given information and answer the questions following it. Three persons A, B and C complete a work in 40 days. B and C together are 5/4 times as efficient as A and B together. On the other hand, A and C together are 7/5 times as efficient as B and C together.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.
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