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.

Correct option is D

Given:
The concentration of wine A = 10%, B = 20%, and C = 30%.
They are mixed in the ratio 2 : 3 : x, resulting in a 23% concentration solution.
Formula Used:
The weighted average concentration formula is:
​$$\text{Final concentration} = \frac{\text{(Part of A) * (Concentration of A) + (Part of B) * (Concentration of B) + (Part of C) * (Concentration of C)}}{\text{Total parts of A, B, and C}}$$​​
Solution:
The total parts of A, B, and C = 2 + 3 + x.
23 =$$\frac{2 \times 10 + 3 \times 20 + x \times 30}{2 + 3 + x}$$​​

23 × (5 + x) = 2 × 10 + 3 × 20 + x × 30

23 × (5 + x) = 20 + 60 + 30x

115 + 23x = 80 + 30x
115 - 80 = 30x - 23x
35 = 7x
x = 35 / 7
x = 5