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:

• A. 120 litres
• B. 100 litres
• C. 150 litres
• D. 75 litres

Answer: (A)

w i n e ( l e f t ) w i n e ( a d d e d )   =   343 169   It means  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 )   =   343 512     (since 343 + 169 = 512)    Thus,   343 x   =   512 x 1   -   15 k 3     343 512   =   7 8 3   =   1   -   15 k 3     1 - 15 k = 7 8 = 1 - 1 8    Thus the initial amount of wine was 120 liters.