The concentration of three wines A, B and C are 10%, 20% and 30%, respectively. They are mixed in the ratio 2 ∶ 3 ∶ x resulting in a 23% concentration solution. Find the value of x.
5
Given:
Concentration of Wine A = 10%
Concentration of Wine B = 20%
Concentration of Wine C = 30%
Ratio of mixture = 2 ∶ 3 ∶ x
Resulting concentration = 23%
Used formula:
Weighted average concentration = (C A × W A + C B × W B + C C × W C) / (W A + W B + W C)
Where CA, CB, and CC are the concentrations of A, B, and C respectively, and WA, WB, and WC are the weights of A, B, and C respectively.
Calculation:
Let the weights be 2, 3, and x respectively.
Resulting concentration = (10 × 2 + 20 × 3 + 30 × x) / (2 + 3 + x)
⇒ 23 = (20 + 60 + 30x) / (5 + x)
⇒ 23 × (5 + x) = 80 + 30x
⇒ 115 + 23x = 80 + 30x
⇒ 115 - 80 = 30x - 23x
⇒ 35 = 7x
⇒ x = 5
∴ The value of x is 5.
Important Questions from Mixture Problems
In a mixture of liquid ,1/5 part is acid 2/5 part is alcohol and the remaining part is water. If the total quantity of the mixture is 20 litres, then how much water (in litre) does the mixture contain?
In what ratio, should rice at ₹60 per kg be mixed with rice at ₹42 per kg such that by selling the mixture at ₹56 per kg there is a gain of 12%?
A vessel contains 20 litres containing milk and water in the ratio 3 : 2. Ten litres of this milk is removed and replaced with equal amount of pure milk. If this process is repeated once again, find the final ratio of milk and water.
From a container of 50 liters pure milk, 10 liters is taken out and replaced by 10 liters of water. If this process is repeated thrice, what is the ratio of water and milk finally?
Consider the following statements about a mixture and determine which of the statements is/are correct.
1. A mixture has a variable composition.
2. In compounds, the composition of each new substance is always fixed.
3. A mixture shows the properties of the constituent substances.
