Which information are sufficient to answer the question asked? P,Q and R working together can complete a work in how many days ? Statement I: P can complete the work in 4 days and Q can complete the same work in 3 days. Statement II: The ratio of their efficiencies of P, Q and R is 3:4:2 respectively. Statement III: R can do as much work in 3 days as P can do in 2 days.

Statement I alone: P's rate = 1/4, Q's rate = 1/3. Without R's rate, can't find combined time. I and II: P, Q, R efficiency ratio 3:4:2. P = 3 units = 1/4, so 1 unit = 1/12. Q = 4 units = 1/3, R = 2 units = 1/6. Combined rate = 1/4 + 1/3 + 1/6 = (3+4+2)/12 = 9/12 = 3/4. Time = 4/3 days. I and III: R does in 3 days what P does in 2. So R's rate = (2/3) × P's rate = (2/3) × (1/4) = 1/6. Combined rate = 1/4 + 1/3 + 1/6 = 3/4. Time = 4/3 days. II and III: R = 2 units (from II), P = 3 units (from II). III says R in 3 days = P in 2 days, which is consistent but gives no absolute rates. Without absolute rate, can't find time. Therefore I and II or I and III are sufficient.