If 20 typists can type 480 pages in 6 hours. How many pages will be typed by 25 typists in 4 hours?

Options

A. 256
B. 576
C. 900
D. 400

Answer

To solve the problem, we can use the concept of work done, which is the product of the number of typists, the time they work, and the rate at which they type.

### Step-by-Step Solution:

1. **Calculate the work done by the initial group of typists:**
- We know that 20 typists can type 480 pages in 6 hours.
- The total work done (in pages) can be calculated as:
\[ \text{Work} = \text{Number of Typists} \times \text{Time} = 20 \text{ typists} \times 6 \text{ hours} = 120 \text{ typist-hours} \]
- Therefore, the rate of typing per typist per hour is:
\[ \text{Rate} = \frac{\text{Total Pages}}{\text{Total Typist-Hours}} = \frac{480 \text{ pages}}{120 \text{ typist-hours}} = 4 \text{ pages per typist per hour} \]

2. **Calculate the work done by the new group of typists:**
- Now, we need to find out how many pages will be typed by 25 typists in 4 hours.
- First, calculate the total typist-hours for this group:
\[ \text{Total Typist-Hours} = 25 \text{ typists} \times 4 \text{ hours} = 100 \text{ typist-hours} \]
- Using the rate we calculated earlier, the total number of pages typed by this group is:
\[ \text{Pages Typed} = \text{Rate} \times \text{Total Typist-Hours} = 4 \text{ pages per typist per hour} \times 100 \text{ typist-hours} = 400 \text{ pages} \]

### Final Answer:
Thus, the number of pages that will be typed by 25 typists in 4 hours is **400 pages**.

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