Alligations and Mixtures Quiz Set 010

The volume of milk will remain same at ${58 × 400}/100$ = 232 liters. The amount of water at present is 400 - 232 = 168 liters. We need to make the volume of water equal to that of the milk. So we have to add 232 - 168 = 64 liters of water.

If a sample n₁ has a weighted average of A₁, and another sample n₂ has a weighted average of A₂, then the weighted average, A,of the combined samples is determined by the alligation formula as: n₁(A - A₁) = n₂(A₂ - A). Putting n₁ = 30, A₁ = 13, n₂ = 60 and A₂ = 7, we get A = 9 Kg.

The water will be sold at the price of wine. So the profit will be earned by selling water as wine. Profit% = $\text"Profit"/\text"Cost"$ × 100. If profit percent is 20%, then 1 part of pure water is sold at the cost of 5 parts of wine. So the required mixing ratio should be 1 : 5.

If a sample n₁ has an average price of A₁, and another sample n₂ has an average price of A₂, then the price of the mixture, A, is determined by the alligation formula as: n₁(A - A₁) = n₂(A₂ - A). Putting A₂ = 20, A₁ = 23, n1 = 24, n2 = 12, we have 24 × (A - 23) = 12 × (20 - A), from where we get A = Rs. 22 per liter.

We shall use the alligation formula. If a sample n₁ has an average property of A₁, and another sample n₂ has an average property of A₂, then the average property of the mixture, A, is determined by the alligation formula as: n₁(A - A₁) = n₂(A₂ - A). Putting A₂ = 2, A₁ = 19, n1 = 13, n2 = 4, we have 13 × (A - 19) = 4 × (2 - A), from where we get A = 15 km/h. The "property" in the alligation formula could be speed, weight, price, etc.,