# A can do a piece of work in 10 days, B can do it in 15 days. They started work together. After 3 days B left from the work and C joined. After 2 days the remaining work was finished. Then in how many days the work could be finished by C alone?

+1 vote

Let the total work be 30 units. Now capacity of A is 3 and B is 2.
They worked for 3 days. So 15 units of work will be completed. Now Remaining work of 15 units completed by A and C in 2 days. So capacity of A and C is 7.5 units. So C capacity is 7.5 - 3 = 4.5 of 9/2
So C can complete the work in 30 / (9/2) = 20/3 = $6\displaystyle\frac{2}{3}$