Institution: Bangladesh Bank Exam: Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, let’s denote the amount of work completed by A, B, and C in one day as \(A\), \(B\), and \(C\) respectively.

From the problem, we have the following equations based on the time taken to complete the work together:

1. \( A + B = \frac{1}{12} \) (A and B together can do the work in 12 days)
2. \( B + C = \frac{1}{20} \) (B and C together can do it in 20 days)
3. \( C + A = \frac{1}{15} \) (C and A together can do it in 15 days)

Now, we can add all three equations together:

\[
(A + B) + (B + C) + (C + A) = \frac{1}{12} + \frac{1}{20} + \frac{1}{15}
\]

This simplifies to:

\[
2A + 2B + 2C = \frac{1}{12} + \frac{1}{20} + \frac{1}{15}
\]

Calculating the right-hand side, we first find a common denominator (which is 60):

\[
\frac{1}{12} = \frac{5}{60},\quad \frac{1}{20} = \frac{3}{60},\quad \frac{1}{15} = \frac{4}{60}
\]

Adding these fractions:

\[
\frac{5 + 3 + 4}{60} = \frac{12}{60} = \frac{1}{5}
\]

Thus,

\[
2A + 2B + 2C = \frac{1}{5}
\]

Dividing both sides by 2 gives:

\[
A + B + C = \frac{1}{10}
\]

This means A, B, and C together can complete the work in 10 days. Therefore, the correct answer is D) 10 days.