Alligation or Mixture problems
A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Let C.P. of 1 liter milk be Re. 1, Gain = 16 2/3 % = 50/3 %and S.P. of 1 liter mixture = Re. 1 then C.P. of 1 liter mixture = (1 x (100 x 3) / 350) = Re. (6 / 7) By the rule of alligation,Hence, required ratio = (1/ 7) : (6 / 7) = 1 : 6
According to question , Total C. P. of 200 kg of mixture = Rs. (80 × 6·75 + 120 × 8)Total C. P. of 200 kg of mixture = Rs. 1500Average rate = Rs. 7·50 per kgRequired rate = 120% of Rs. 7·50Required rate = Rs. 9 per kg.
As given equal amounts of alloys are melted, let it be 1 kg. Required ratio of gold and silver = 5 13 + 5 8 8 13 + 3 8 = 105 103 . Hence, ratio of gold and silver in the resulting alloy = 105/103.
EXAMIANS