Alligation or Mixture problems
Tea worth of Rs. 135/kg & Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?
Suppose the vessel initially contains 8 litres of liquid. Let x litres of this liquid be replaced with water. Quantity of water in new mixture = ❨ 3 - 3x + x ❩ litres 8 Quantity of syrup in new mixture = ❨ 5 - 5x ❩ litres 8 ∴ ❨ 3 - 3x + x ❩ = ❨ 5 - 5x ❩ 8 8 ⟹ 5x + 24 = 40 - 5x ⟹ 10x = 16 ⟹ x = 8 . 5 So, part of the mixture replaced = ❨ 8 x 1 ❩ = 1 . 5
% 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
Average speed = (100 / 10) = 10 km/hr. Ratio of time taken at 7 km/hr to 12 km/hr = 2 : 3 Time taken at 7 km/hr = 2 (2 + 3) × 10 = 4 hrs. Distance covered at 7 km/hr = 7 × 4 = 28 km. Distance covered at 12 km/hr = 100 ? 28 = 72 km.
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.