Rohan can alone finish a work in 12 days and Hari can alone in 16 days. They both work for 3 days and then Rohan left. After that only Hari works and finishes the work. The total work will be completed in:

Given:

Rohan can finish a work in 12 days.

Hari can finish the same work in 16 days.

They both work together for 3 days.

Rohan leaves and Hari finishes the remaining work alone.

Concept:

Work done by an individual in 1 day is the reciprocal of the total days they take to complete the work.

Formula Used:

Work done by Rohan in 1 day = 1/12

Work done by Hari in 1 day = 1/16

Total Work = 1 (assuming the whole work is 1 unit)

Calculation:

Work done by Rohan and Hari together in 1 day:

⇒ (1/12) + (1/16)

⇒ (4 + 3)/48

⇒ 7/48

Work done by Rohan and Hari together in 3 days:

⇒ 3 × (7/48)

⇒ 21/48

⇒ 7/16

Remaining work after 3 days:

⇒ 1 - 7/16

⇒ 9/16

Time taken by Hari to complete the remaining work:

⇒ (9/16) × 16

⇒ 9 days

Total time taken to complete the work:

⇒ 3 days (together) + 9 days (Hari alone)

⇒ 12 days

∴ The total work will be completed in 12 days.