John can complete a work in 9 days, whereas John and Smith together can complete the same work in 6 days. How long will it take for Smith alone to complete the work?

John can complete a work in 9 days, whereas John and Smith together can complete the same work in 6 days. How long will it take for Smith alone to complete the work? Correct Answer 18 Days

Time taken by John = 9 days

Time taken by John and Smith = 6 days

Let the total work be LCM of 9 and 6 = 54 unit

Work done by John in 1 day = 54/9 = 6 unit

Work done by John and Smith in 1 day = 54/6 = 9 unit

Time taken by Smith to complete the work alone = 54/(9 - 6) = 18 days

Related Questions

In how many days will Robert alone complete 3/5th of the work? I: James alone can do the work in 40 days. John is 300% more efficient than James. The ratio of efficiency between Michael and James is 8 : 3. Robert is 25% less efficient than Michael. II: John and Robert together can finish the work in \(6\frac{2}{3}\;\)days, Robert and Michael in \(8\frac{4}{7}\;\)days, Michael in  and John can do the same work in 6 days.