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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.

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. Correct Answer The data either in statement I alone or in statement II alone are sufficient to answer the question.

Concept:

Efficiency is inversely proportional to the time taken when the amount of work done is constant.

Total work (in units) = Number of days × Number of units completed per day (Efficiency)

Calculation:

From statement I:

Ratio of efficiency, John : James = 4 : 1 = 12 : 3

Michael : James = 8 : 3

Robert : Michael = 3 : 4 = 6 : 8

∴ The ratio of efficiency, John : James : Michael : Robert = 12 : 3 : 8 : 6

∴ Total work = 40 × 3 = 120 units

According to question,

3/5th of the total work = 3/5 × 120 = 72 units

One day work of Robert = 6 units

∴ Time taken by Robert to complete 3/5th of the work = 72/6 = 12 days

Statement I alone is sufficient to find the answer.

From Statement II:

John + Robert = 20/3 days

Robert + Michael = 60/7 days

Michael + John= 6 days

Suppose the total work = LCM (20/3, 60/7, 6) = 60 units

One day work of John + Robert = 60/(20/3) = 9 units

One day work of Robert and Michael = 60/(60/7) = 7 units

One day work of Michael and John = 60/6 = 10

∴ One day work of John, Robert and Michael = (1/2) × (9 + 7 + 10) = 13

∴ One day work of Robert = 13 – 10 = 3 units

According to question,

3/5th of the total work = 3/5 × 60 = 36 units

One day work of Robert = 3 units

∴ Time taken by Robert to complete 3/5th of the work = 36/3 = 12 days

Statement II alone is also sufficiency to find the answer.

∴ The data either in statement I alone or in statement II alone are sufficient to answer the question.

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