Institution: AGRANI BANK LTD Exam: Agrani bank Ltd - Officer 04.07.2008
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To find the percentage of the task completed by Faruk and his two assistants in 5 days, we first need to determine their work rates.

Faruk can complete the task in 20 days, so his work rate is \( \frac{1}{20} \) of the task per day. Each assistant works at half Faruk's speed, meaning they each complete \( \frac{1}{40} \) of the task per day.

Now, let's find the combined work rate of Faruk and his two assistants. The total work done per day is:

\[
\text{Faruk's rate} + \text{Assistant 1's rate} + \text{Assistant 2's rate} = \frac{1}{20} + \frac{1}{40} + \frac{1}{40}
\]

To add these fractions, we need a common denominator, which is 40:

\[
\frac{1}{20} = \frac{2}{40} \quad \text{(Faruk's rate)}
\]
\[
\frac{1}{40} = \frac{1}{40} \quad \text{(Assistant 1's rate)}
\]
\[
\frac{1}{40} = \frac{1}{40} \quad \text{(Assistant 2's rate)}
\]

Adding these:

\[
\frac{2}{40} + \frac{1}{40} + \frac{1}{40} = \frac{4}{40} = \frac{1}{10}
\]

This means together, they complete \( \frac{1}{10} \) of the task per day.

In 5 days, their total work is:

\[
5 \times \frac{1}{10} = \frac{5}{10} = \frac{1}{2}
\]

This indicates they complete half of the task in 5 days, which corresponds to 50%. Therefore, the correct answer is option C: 50%.