Manoj can type 100 pages of a report in 10 hours and Bobby can do the same in 15 hours. They worked together for 5 hours. The remaining work was completed by Lucy in 2 hrs. if they received Rs. 2,400 for whole work, Lucy got

First, let us determine the rate of typing for Manoj and Bobby:
* Manoj's typing speed = $\frac{100\text{pages}}{10\text{hours}}=10\text{pages/hour}$
* Bobby's typing speed = $\frac{100\text{pages}}{15\text{hours}}=\frac{20}{3}\text{pages/hour}$

They worked together for $5\text{hours}$, so the number of pages they completed is:

$$\text{Pages completed}=5\times \left(10+\frac{20}{3}\right)=5\times \left(\frac{50}{3}\right)=\frac{250}{3}\text{pages}$$

The remaining number of pages left to be completed is:

$$\text{Remaining pages}=100-\frac{250}{3}=\frac{50}{3}\text{pages}$$

Lucy finishes this remaining work of $\frac{50}{3}\text{pages}$ in $2\text{hours}$.
Since wages are distributed based on the total fraction of work done by each individual, we compute Lucy's share using the ratio of pages she typed to the total pages ($100$):

$$\text{Lucy’s work fraction}=\frac{\frac{50}{3}}{100}=\frac{50}{300}=\frac{1}{6}$$

The total amount paid for the entire report is $\text{Rs. }2,400$. Thus, Lucy's payment is:

$$\text{Lucy’s share}=\frac{1}{6}\times 2,400=\text{Rs. }400$$