Alligation or Mixture problems
A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Suppose the can initially contains 7x and 5x of mixtures A and B respectively. Quantity of A in mixture left = ❨ 7x - 7 x 9 ❩ litres = ❨ 7x - 21 ❩ litres. 12 4 Quantity of B in mixture left = ❨ 5x - 5 x 9 ❩ litres = ❨ 5x - 15 ❩ litres. 12 4 ∴ ❨ 7x - 21 ❩ 4 = 7 ❨ 5x - 15 ❩ + 9 4 9 ⟹ 28x - 21 = 7 20x + 21 9 ⟹ 252x - 189 = 140x + 147 ⟹ 112x = 336 ⟹ x = 3. So, the can contained 21 litres of A.
Let the amount of juice and water in original mixture '4x' litre and '3x' litre respectively.
According to given data,
4x / 3x + 6 = 8/7
28x = 24x + 48
28 x ? 24x = 48
4x = 48
x = 12
Amount of juice = 4x = 4×12 = 48 litre.
Milk Water 74% 26% (initially) 76% 24% ( after replacement) Left amount = Initial amount 1 - r e p l a c e d a m o u n t t o t a l a m o u n t 24 = 26 1 - 7 k => k = 91
% of milk in first bottle = 64% % of milk in second bottle = 100 - 26 = 74% Now, ATQ 64% 74% 68% 6 4 Hence, by using allegation method, Required ratio = 3 : 2