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Let the initial amount of wine be $x$.

$x - 15 - 15 - 15 : 15+ 15 + 15 = 343: 169$

$x - 45 : 45 = 343:169$

$x = \frac{343 \times 45}{169} + 45$

$=45 \times \left[ \frac{343}{169} + 1\right]$

$=45 \times \frac{512}{169}$

$=136.33$

The above approach is wrong because after the first replacement, we are no longer having pure wine but a mixture of wine and water.

Amount of wine remaining $= \frac{343x}{343+169} = \frac{343x}{512}.$

Amount of wine after first add/remove $= x - 15 = x\left(1-\frac{15}{x}\right)$, after second add/remove $=x\left(1-\frac{15}{x}\right)^2$ and similarly after the third add/remove $x\left(1-\frac{15}{x}\right)^3$.

Thus we get $\frac{343x}{512} = x\left(1-\frac{15}{x}\right)^3$

$\implies \frac{7}{8} = 1 - \frac{15}{x}$

$\implies \frac{15}{x} = \frac{1}{8}$

$\implies x = 15 \times 8 = 120.$