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
If the ratio of alcohol and water in a mixture of 85 litres is 11 ∶ 6. How much water should be added to make the ratio 5 ∶ 3?
Two bottles A and B contain diluted acid. In bottle A, the amount of water is double the amount of acid while in bottle B, the amount of acid is 3 times that of water. How much mixture(in litres) should be taken from each bottle A and B respectively in order to prepare 5 liters diluted acid containing an equal amount of acid and water?
A solution of milk and water contains milk and water in the ratio of 3 : 2. Another solution of milk and water contains milk and water in the ratio of 2 : 1. Forty litres of the first solution is mixed with 30 litre of the second solution. The ratio of milk and water in the resultant solution is:
A 70 litre mixture has liquids A and B in the ratio 5 ∶ 9. How many litres of liquid A must be added so that the ratio becomes 2 ∶ 3?
In a mixture of 60 litres, the ratio of milk and water is 2 : 1 respectively. How much more water must be added to make its ratio 1 : 2 respectively?
