The concentrations 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.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 5.
Given:
The concentrations of three wines (A, B, and C) are 10%, 20%, and 30%, respectively.
They are mixed in the ratio of 2 : 3 : x in a 23% concentration solution.
Calculations:
Let the concentration of A, B, and C be 20k, 30k, and 10xk respectively
Total mixture initially = 20k + 30k + 10xk = 10k(5 + x)
According to the question;
A = 20k × 10/100 = 2k
B = 30k × 20/100 = 6k
C = 10xk × 30/100 = 3xk
Total wine solution = (2k + 6k + 3xk) = (8 + 3x)k
Now,
⇒ (8 + 3x)k/10k(5 + x) = 23/100
⇒ (8 + 3x) × 100 = 230 × (5 + x)
⇒ 300x + 800 = 1150 + 230x
⇒ 70x = 350
⇒ x = 5