A report of 100 pages is to be typed by three typists. Typist A can type 100 pages in 10 hours. Typist B can type the same pages in 20 hours and typist C in 25 hours. All the three typist started typing at 09·00 a.m. At 01·00 p.m. typist A stopped typing. The other two typists finished the job, approximately at what time the report was typed ?

Options

A. `2.40 p.m.`
B. `5.00 p.m.`
C. `6.00 p.m.`
D. `3.40 p.m.`

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the typing speed of each typist
- Typist A can type 100 pages in 10 hours, so A's speed is:
\[ \text{Speed of A} = \frac{100 \text{ pages}}{10 \text{ hours}} = 10 \text{ pages/hour} \]

- Typist B can type 100 pages in 20 hours, so B's speed is:
\[ \text{Speed of B} = \frac{100 \text{ pages}}{20 \text{ hours}} = 5 \text{ pages/hour} \]

- Typist C can type 100 pages in 25 hours, so C's speed is:
\[ \text{Speed of C} = \frac{100 \text{ pages}}{25 \text{ hours}} = 4 \text{ pages/hour} \]

### Step 2: Calculate the number of pages typed by Typist A in 4 hours
- Typist A works from 9:00 a.m. to 1:00 p.m. for 4 hours. The number of pages typed by A is:
\[ \text{Pages typed by A} = \text{Speed of A} \times \text{Time} = 10 \text{ pages/hour} \times 4 \text{ hours} = 40 \text{ pages} \]

### Step 3: Calculate the remaining pages
- Total pages are 100, and A typed 40 pages, so the remaining pages are:
\[ \text{Remaining pages} = 100 - 40 = 60 \text{ pages} \]

### Step 4: Determine how long it will take for Typists B and C to finish the remaining pages
- Let \( H \) be the time in hours that B and C work together to finish the remaining 60 pages. The combined work done by B and C in \( H \) hours is:
\[ \text{Pages typed by B} = 5H \quad \text{and} \quad \text{Pages typed by C} = 4H \]
- Therefore, the equation becomes:
\[ 5H + 4H = 60 \]
\[ 9H = 60 \]
\[ H = \frac{60}{9} = \frac{20}{3} \text{ hours} \approx 6.67 \text{ hours} \]

### Step 5: Convert hours to hours and minutes
- \( \frac{20}{3} \) hours is equal to 6 hours and 40 minutes.

### Step 6: Calculate the finishing time
- Typist A stops at 1:00 p.m. B and C continue for 6 hours and 40 minutes. Therefore, the finishing time is:
\[ 1:00 \text{ p.m.} + 6 \text{ hours} + 40 \text{ minutes} = 7:40 \text{ p.m.} \]

### Final Answer
The report was typed by approximately **7:40 p.m.**

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