There are 4 friends A, B, C and
D. The ratio of efficiency of C and D to complete a work is 3:4 and that of A and B is 1:2. Find the time taken by D alone to finish the work.
I. A and D together can complete the work in 6 days.
II. A, B and C together can complete the same work in 5 days.
III. B and D together can complete the work in 5 days.

ATQ, Let A do a units/day and B do 2a units/day. Let C do 3b units/day and D do 4b units/day. From I: Total work W = 6(a + 4b) …(1) From II: Total work W = 5(a + 2a + 3b) = 5(3a + 3b) …(2) From III: Total work W = 5(2a + 4b) …(3) From I alone, we know W in terms of a and b, but cannot get D alone. From II alone, again only one equation in a and b. From III alone, also only one equation. But using any two equations, e.g. (1) and (2), we can equate W and get a relation between a and b, and then find W and D’s time = W/(4b). Similarly, (2) and (3) or (1) and (3) are also sufficient. Hence, any two statements together are sufficient.