A can do a job in 10 days and B can do it in 15 days. If they work together, how long will it take them to complete the job? ​​

Given: 

A can do a job in 10 days and B can do it in 15 days.

Solution: 

Work done by A in 1 day = $$\frac {1}{10}$$​​

Work done by B in 1 day = $$\frac {1}{15}$$​​

Together in 1 day = $$\frac {1}{10}$$​ + $$\frac {1}{15}$$​​
LCM of 10 and 15 = 30
So = $$\frac {3}{30}$$​ + $$\frac {2}{30}$$​ = $$\frac {5}{30}$$​ = $$\frac {1}{6}$$​​

That means A and B together complete $$\frac {1}{6}$$​ of the job per day.
So, total time to finish = 6 days.

Thus, correct option is (b).