There is a simple trick here to solve problems on work and time faster
First we have to take the LCM of the days both people take to complete a piece of work ie., LCM of 15,10 = 30.
Now this leads to 2 ratios 30/15 = 2 and 30/10 = 3 which represents thier work speed (higher = faster) also 30 represents the total work that needs to be done.
So for this problem both of them are working together for 2 days. So thier speed = 3+2 = 5/day. Therefore total work done after 2 days = 10, which is 1/3rd of the total work done. So the amount work left to be done = 2/3rd.