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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:

75 litres
100 litres
150 litres
120 litres

Correct Answer: 120 litres

Explanation:

$\frac{w i n e (l e f t)}{w i n e (a d d e d)} = \frac{343}{169}$

It means $\frac{w i n e (l e f t)}{w i n e (i n i t i a l a m o u n t)} = \frac{343}{512}$ (since 343 + 169 = 512)

Thus, $343 x = 512 x 1 - \frac{15}{k} 3$

$\frac{343}{512} = \frac{7}{8} 3 = 1 - \frac{15}{k} 3$

$1 - \frac{15}{k} = \frac{7}{8} = 1 - \frac{1}{8}$

Thus the initial amount of wine was 120 liters.

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