A and B can do a work in 12 days and 18 days respectively They worked together for 4 days after whic...........

Quantitative Aptitude (MTS) Time & distance

A and B can do a work in 12 days and 18 days, respectively. They worked together for 4 days, after which B was replaced by C

and the remaining work was completed by A and C in the next 4 days. In how many days will C alone complete the same work?

This questions was previously asked in

SSC MTS 26th October 2021 Shift-3

- Efficiency Calculation:

- A's Work Rate: A completes 1/12 of the work per day.

- B's Work Rate: B completes 1/18 of the work per day.

- Work Done by A and B Together for 4 Days:

- Combined rate per day = 1/12 + 1/18 = 5/36 of the work.

- In 4 days, they complete (5/36) * 4 = 20/36 = 5/9 of the work.

- Remaining Work:

- Total work - completed work = 1 - 5/9 = 4/9.

- A and C's Combined Work:

- They complete 4/9 of the work in 4 days.

- Combined rate = (4/9) / 4 = 1/9 of the work per day.

- Finding C's Work Rate:

- A's rate = 1/12, so C's rate must be 1/9 - 1/12 = 1/36.

- Time for C Alone:

- C would take 1/(1/36) = 36 days to complete the work alone.

- Conclusion:

- Correct Option: 4 - 36

- The correct answer is option: 4 - 36

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