From a container of wine, a thief has stolen 15 liters 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 amount of wine in the container be x liters.
• In each operation, 15 liters of wine is removed and replaced by 15 liters of water.
• This is a classic replacement problem and follows the formula:
  Final quantity of wine = x × (1 – r/x)ⁿ
  where r is the quantity removed and replaced each time, and n is the number of repetitions.
• Here, r = 15, n = 3, and final ratio of wine to water = 343 : 169
• So, final wine = x × (1 – 15/x)³ = (343/512) × x

Set up the equation:

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)
1 – 15/x = 7/8

Solve the equation:

1 – 7/8 = 15/x
1/8 = 15/x
x = 15 × 8 = 120

Answer: 120 liters

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