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
A mixture of acid and water contains 20 percent acid. When 10 litres of water is added to the mixture, then the percentage of acid becomes 15 percent. What is the original quantity of mixture ?
A container contains 20 L mixture in which there is 10% sulphuric acid. Find the quantity of sulphuric acid to be added in it to make the solution to contain 25% sulphuric acid.
The ratio of milk to water in a 100 litres mixture is 2 ∶ 3. 10 litres of this mixture is withdrawn and replaced with milk. This process is repeated 2 more times, What is the percentage of milk in final mixture ?
- 80% and 90% pure acid solutions are mixed to obtain 20 litres of 87% pure acid solution. Find the quantity (in litres) of 80% pure acid solution taken to form the mixture.
Some fruits are bought at a rate of 11 for Rs. 100 and an equal number at a rate of 9 for Rs. 100. If all the fruits are sold at a rate of 10 for Rs. 100, then what is the gain or loss percent in the entire transaction?
