Given :- A can complete 40% of a work in 16 days . B is 25% LESS efficient than C . C takes 16 days less than A to complete the work. In how many days A and B TOGETHER can complete 84.375% of work together ?

SOLUTION :-

→ A can complete 40% of a work in = 16 days .

so,

→ A can complete 100% of a work in = (16/40) * 100 = 40 days .

now,

→ Time taken by C to complete the work = 16 days less than A = 40 - 16 = 24 days .

then,

→ Time taken by B to complete the work = (24 * 100)/75 = 32 days .

now,

→ LCM of (40 and 32) = 160 units = Let total work .

so,

→ Efficiency of A = Total work / time taken = 160/40 = 4 units / day

→ Efficiency of B = Total work / time taken = 120/32 = 5 units / day

then,

→ Efficiency of (A + B) = 4 + 5 = 9 units / day.

therefore,

→ Time taken by A and B to complete 84.375% of work together = (160 * 84.375/100) / 9 = 135 / 9 = 15 days (Ans.)

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