Alligation or Mixture problems
Ratio of water and milk in a container is 2 : 3. If 40 liter mixture removed from the container and same quantity of milk is added to it then the ratio of water to milk becomes 1 : 4. Find the initial quantity of mixture?
From the given data, let the initial quantity of the mixture = 5x Then, 2 x - 16 3 x - 24 + 40 = 1 4 8 x - 64 = 3 x + 16 5 x = 80 x = 16 lit Then the initial quantity of the mixture = 5x = 5 x 16 = 80 lit.
Let the price of the mixed variety be Rs. x per kg. By rule of alligation, we have: Cost of 1 kg of Type 1 rice Cost of 1 kg of Type 2 rice Rs. 15 Mean Price Rs. x Rs. 20 (20 - x) (x - 15) ∴ (20 - x) = 2 (x - 15) 3 ⟹ 60 - 3x = 2x - 30 ⟹ 5x = 90 ⟹ x = 18.
Let the price per kg of mixed variety be Rs. P; then By the rule of alligation,Now, (20 - P) / (P - 15) = (2 / 3) ? 60 ? 3P = 2P ? 30 ? 5P = 90 ? P = Rs. 18
As per the given question , We are concerned with solid part of the fruit (pure portion). Assume Q kg of dry fruit is obtained.? Solid part in fresh fruit = Solid part in dry fruit? 0·28 × 100 = 0·8 × Q? Q = 35 kg? 35 kg of dry fruit can be obtained from 100 kg fresh fruit.
Copper in 4 kg = 4/5 kg and Zinc in 4 kg = 4 x (4/5) kg Copper in 5 kg = 5/6 kg and Zinc in 5 kg = 5 x (5/6) kg Therefore, Copper in mixture = 4 5 + 5 6 = 49 30 kg and Zinc in the mixture = 16 5 + 25 6 = 221 30 kg Therefore the required ratio = 49 : 221
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