Alligation or Mixture problems
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:
W i n e ( l e f t ) W a t e r ( 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 ? 343 + 169 = 512 Thus , 343 x = 512 x 1 - 15 K 3 ? 343 512 = 7 8 3 = 1 - 15 k 3 => K = 120 Thus the initial amount of wine was 120 liters.
By the rule of alligation, we have: Strength of first jar Strength of 2nd jar 40% MeanStrength 26% 19% 7 14 So, ratio of 1st and 2nd quantities = 7 : 14 = 1 : 2 ∴ Required quantity replaced = 2 3