Dinesh and Rakesh are working on an Assignment, Dinesh takes 6 hours to type 32 pages on a computer, while Rakesh takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 page?
दिनेश और राकेश किसी परियोजना पर काम कर रहे हैं। दिनेश कम्प्यूटर पर 6 घंटे में 32 पृष्ठ टाइप करता है जबकि राकेश 5 घंटे में 40 पृष्ठ टाइप करता है। दोनों मिलकर 110 पृष्ठों की परियोजना को अलग-अलग कम्प्यूटर पर कितने समय में टाइप करेंगे?

Options

A. 7 hrs, 30 min
B. 8 hrs
C. 8 hrs, 15 min
D. 8 hrs, 25 min

Explanation

To solve the problem of how much time Dinesh and Rakesh will take to type 110 pages together, we can follow these steps:

### Step 1: Calculate Dinesh's typing rate
Dinesh takes 6 hours to type 32 pages.
To find his typing rate (pages per hour), we use the formula:

\[ \text{Dinesh's typing rate} = \frac{\text{Total pages}}{\text{Total time}} = \frac{32 \text{ pages}}{6 \text{ hours}} \approx 5.33 \text{ pages/hour} \]

### Step 2: Calculate Rakesh's typing rate
Rakesh takes 5 hours to type 40 pages.
Similarly, we calculate his typing rate:

\[ \text{Rakesh's typing rate} = \frac{40 \text{ pages}}{5 \text{ hours}} = 8 \text{ pages/hour} \]

### Step 3: Calculate their combined typing rate
To find their combined typing rate when working together, we add their individual rates:

\[ \text{Combined typing rate} = \text{Dinesh's rate} + \text{Rakesh's rate} = 5.33 \text{ pages/hour} + 8 \text{ pages/hour} = 13.33 \text{ pages/hour} \]

### Step 4: Calculate the time taken to type 110 pages together
Now, we need to find out how long it will take them to type 110 pages together. We use the formula:

\[ \text{Time} = \frac{\text{Total pages}}{\text{Combined typing rate}} = \frac{110 \text{ pages}}{13.33 \text{ pages/hour}} \approx 8.25 \text{ hours} \]

### Step 5: Convert the time into hours and minutes
To convert 8.25 hours into hours and minutes:
- The whole number part is 8 hours.
- The decimal part (0.25 hours) can be converted to minutes by multiplying by 60:

\[ 0.25 \times 60 = 15 \text{ minutes} \]

Thus, the total time taken is approximately **8 hours and 15 minutes**.

### Final Answer
Dinesh and Rakesh will take **8 hours and 15 minutes** to type the assignment of 110 pages together.

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