- 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.
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