A and B can do a work in 10 days and 15 days respectively. They worked together for 5 days, then B left the work and A alone did the remaining work. The whole work got completed in:

$6\frac{2}{3}$ days

A and B can do a work in 10 days and 15 days respectively.

A's 1 day work = 1/10

B's 1 day work = 1/15

If they work together,

A and B one day work = 1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6

For 5 days = 5* 1/6 = 5/6

Remaining work = 1/6

Time taken by A alone for 1/6 of work = (1/6) / (1/10) = 5/3

Total Time = 5 days + 5/3 days = 20/3 days

The correct answer is Option (1) → $6\frac{2}{3}$ days