Alligation or Mixture problems
In what ratio sugar of Rs 38 per kg and Rs 30 per kg be mixed with each other so that on selling mixture at Rs 35.2 per kg there will be a profit of 10%?
Ratio of milk and water = 2 : 1Quantity of milk = 60 X 2/3 = 40 litreQuantity of water = 20 litreTo make ratio, 1: 2, we have to double the water that of milkSo, water should be 80 litre.That means 80 ? 20 = 60 litre water to be added.
Cost price of the mixture = 15 × (100 / 180) = Rs. 25/3 per kg
(Quantity of rice @ Rs. 8 per kg) / (Quantity of rice @ Rs.10 per kg) = (5 / 3) / (1/3) = 1/5
Quantity of rice @ Rs. 10 per kg = 25 × (1/ 5) = 5 kgs.
Let the quantity of the wine in the cask originally be x litres. Then, quantity of wine left in cask after 4 operations = [ x ❨ 1 - 8 ❩ 4 ] litres. x ∴ ❨ x(1 - (8/x))4 ❩ = 16 x 81 ⟹ ❨ 1 - 8 ❩ 4 = ❨ 2 ❩ 4 x 3 ⟹ ❨ x - 8 ❩ = 2 x 3 ⟹ 3x - 24 = 2x ⟹ x = 24.
Here withdrawal of liquid A and B result into making the container empty. Hence percentage of two liquids withdrawn are two components of the percentage by which the container becomes empty. Applying the rule of alligation, we getA : B = 10 : 20 or 1 : 2 Quantity of liquid = 1 (1 + 2) × 90 = 30 liters Quantity of liquid B = 90 ? 30 = 60 liters.
Rate of rice of quantity 280 kg = Rs. 15.60/kg Rate of rice of quantity 120 kg = Rs. 14.40/kg He want to earn a profit of Rs. 10.45/kg Rate of Mix to sell to get profit of 10.45 = 280 x 15 . 60 + 120 x 14 . 40 280 + 120 + 10 . 45 4368 + 1728 400 + 10 . 45 = > 15 . 24 + 10 . 45 = 25 . 69
EXAMIANS