From a container of wine, a thief has stolen 15 litres of wine and replaced it with same quantity of water. He again repeated the same process. Thus, in three attempts the ratio of wine and water became 343 : 169. The initial amount of wine in the container was:

• Let the initial quantity of wine in the container be x liters.
• The thief steals 15 liters of wine and replaces it with 15 liters of water. This process is repeated 3 times.
• This is a standard replacement problem. The formula to calculate the remaining wine is:
  Final wine quantity = x × (1 - r/x)ⁿ
  where:
  r = quantity removed each time = 15 liters
  n = number of operations = 3
• It is given that the final ratio of wine to water is 343 : 169
• So, final wine = (343 / (343 + 169)) × x = (343 / 512) × x
• According to the replacement formula:
  x × (1 - 15/x)3 = (343 / 512) × x
• Cancel x from both sides:
• (1 - 15/x)3 = 343 / 512
• Take cube root on both sides:
  1 - 15/x = ∛(343 / 512) = 7/8
• ⇒ 1 - 7/8 = 15/x
• ⇒ 1/8 = 15/x
• ⇒ x = 15 × 8 = 120

Answer: 120 liters

The initial quantity of wine in the container was 120 liters.