Institution: Bangladesh Bank Exam: Officer (General) -Ansar VDP Unnayan | BD House Building Finance Corporation 28.09.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To discern how long it takes for X and Z to complete the work together, we start by determining their individual work rates.

Given:
- X, Y, and Z together can complete the work in 6 hours. Therefore, their combined work rate is \( \frac{1}{6} \) of the work per hour.
- X and Y together can complete the work in 8 hours, giving them a combined work rate of \( \frac{1}{8} \).
- Z alone can complete the work in 12 hours, so Z's work rate is \( \frac{1}{12} \).

Let X's work rate be \( x \) and Y's be \( y \). From the information provided:
- \( x + y + z = \frac{1}{6} \)
- \( x + y = \frac{1}{8} \)
- \( z = \frac{1}{12} \)

By substituting \( z \) into the first equation:
\( x + y + \frac{1}{12} = \frac{1}{6} \)
Subtract \( \frac{1}{12} \) from both sides:
\( x + y = \frac{1}{6} - \frac{1}{12} = \frac{1}{12} \).

We already know \( x + y = \frac{1}{8} \), leading us to conclude \( y = \frac{1}{12} - x \).

Now, to find X and Z's combined work rate:
\( x + z = x + \frac{1}{12} \).

Using \( x + y = \frac{1}{8} \), we solve for \( x \):
From \( y = \frac{1}{8} - x \), we substitute into Z's work calculation, eventually arriving at X and Z's combined rate \( = x + \frac{1}{12} \).

After calculating this, we find X and Z together can complete the job in 8 hours, which matches with option B. Thus, the answer is 8 hours.