Albela, Bob and Chulbul have to read a document of seventy eight pages and make a presentation next day. They realize that the article is difficult to understand and they would require team work to finish the assignment. Albela can read a page in 2 minutes, Bob in 3 minutes, and Chulbul in 4 minutes. If they divide the article into 3 parts so that all three of them spend the equal amount of time on the article, the number of pages that Bob should read is

Options

A. 24
B. 25
C. 26
D. 27

Answer

To solve the problem, we need to determine how many pages Bob should read if Albela, Bob, and Chulbul divide the 78 pages evenly based on the time they take to read.

### Step-by-step Solution:

1. **Identify the Reading Rates:**
- Albela can read a page in 2 minutes, so in 1 minute, she reads \( \frac{1}{2} \) pages.
- Bob can read a page in 3 minutes, so in 1 minute, he reads \( \frac{1}{3} \) pages.
- Chulbul can read a page in 4 minutes, so in 1 minute, he reads \( \frac{1}{4} \) pages.

2. **Let the time spent by each person be \( t \) minutes.**
- In \( t \) minutes, the number of pages read by each person will be:
- Albela: \( \frac{t}{2} \) pages
- Bob: \( \frac{t}{3} \) pages
- Chulbul: \( \frac{t}{4} \) pages

3. **Set up the equation for total pages read:**
- The total pages read by all three should equal 78 pages:
\[ \frac{t}{2} + \frac{t}{3} + \frac{t}{4} = 78 \]

4. **Find a common denominator to combine the fractions:**
- The least common multiple (LCM) of 2, 3, and 4 is 12.
- Rewrite the equation using the common denominator:
\[ \frac{6t}{12} + \frac{4t}{12} + \frac{3t}{12} = 78 \]
- Combine the fractions:
\[ \frac{6t + 4t + 3t}{12} = 78 \]
\[ \frac{13t}{12} = 78 \]

5. **Solve for \( t \):**
- Multiply both sides by 12 to eliminate the fraction:
\[ 13t = 78 \times 12 \]
\[ 13t = 936 \]
- Divide by 13:
\[ t = \frac{936}{13} = 72 \text{ minutes} \]

6. **Calculate the number of pages Bob will read:**
- Bob reads \( \frac{t}{3} \) pages:
\[ \text{Pages read by Bob} = \frac{72}{3} = 24 \text{ pages} \]

### Final Answer:
The number of pages that Bob should read is **24 pages**.