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 solve the problem, we start with the initial mixture of milk and water in the ratio of 6:5. This means that in a total of \(6 + 5 = 11\) parts, 6 parts represent milk and 5 parts represent water.

Given that the total mixture is 22 liters, we can calculate the amounts of milk and water:

- Milk: \(\frac{6}{11} \times 22 = 12\) liters
- Water: \(\frac{5}{11} \times 22 = 10\) liters

When 22 liters of the mixture is replaced entirely with water, we subtract the milk and water from the original amounts:

- Remaining milk: \(12 - \frac{6}{11} \times 22 = 0\) liters (since all the mixture is replaced)
- Remaining water: \(10 - \frac{5}{11} \times 22 = 0\) liters (after the mix is removed)

Next, replacing this with water results in:

- Added water = 22 liters
- Total water after replacement = \(22\) liters (from the replacement) + \(0\) liters (remaining water before replacement) = \(22\) liters.

However, after the water is added back, the new ratio of milk to water changes to 9:13. This means that out of 22 new total parts (9 parts milk, 13 parts water), we can calculate:

- Total parts = \(9 + 13 = 22\)
- Water = \(\frac{13}{22} \times (total \ mixture)\).

Now, using the quantity of water, we find that the total amount of water in the mixture is \(13/(9+13) * (water before replacement)\), substituting into our amounts:

Thus, the percentage of water becomes \(13/(9+13) * 22 = 52\) liters.

Hence, after replacement, the total quantity of water is 52 liters, confirming the correct answer (D: 52 liters).