P and Q can finish a work in 15 and 10 days respectively. If Q starts the work and leaves after 5 days, how many days will it take for P to complete the remaining work?

To determine how long it will take for P to finish the remaining work after Q has started it, we first need to calculate the amount of work done by both P and Q.

Q can complete the entire work in 10 days, which means Q can do ( \frac{1}{10} ) of the work in one day. After working for 5 days, Q will have completed:

[

5 \times \frac{1}{10} = \frac{5}{10} = \frac{1}{2}

]

Therefore, Q has completed half of the work in those 5 days.

This leaves P to complete the remaining half of the work. P can complete the entire work in 15 days, meaning P can do ( \frac{1}{15} ) of the work in a single day. To find the number of days it would take for P to complete the remaining half of the work, we set up the equation:

[

\text{Remaining work} = \frac{1}{2}

]

Let ( x ) be the number of days P needs. In ( x ) days, P will complete:

[

x \times \frac{1}{