GIVEN: P completes a work in 30 days and works on first day Q completes a work in 15 days and works on Second day R completes a work in 20 days and works on third day After that again P works for one day then Q works for next day and R works for next to next day and so on. CONCEPT: First we calculate work completed by individual per day then we calculate work completed by single men in successive days Calculation: LCM of 30, 15, 20 = 60 Let the total work be 60 units Efficiency of P = 60 / 30 = 2 units Efficiency of Q = 60 / 15 = 4 units Efficiency of R = 60 / 20 = 3 units According to question 1st day P come on work 2nd day Q come on work and 3rd day R come on work Work complete on 1st day = 2 units Work complete on 2nd day = 4 units Work complete on 3rd day = 3 units So, total work completed in 3 days = (2 + 4 + 3) = 9 units We can take this 3 days work as 1 cycle ∴ in 6 cycles work completed = 9 × 6 = 54 units Remaining work = 60 units – 54 units = 6 units (1 cycle = 3 days) ∴ 6 cycles = 6 × 3 = 18 days 19th day P come on work Work done by P on 19th day = 2 units Work left after 19 days = 60 – 56 = 4 units Q work on 20th day Efficiency of Q = 4 units Q complete the remaining work on 20th day Total time taken to complete the work = 20days