Question
The concentrations of three acids, A, B, and C, are
specified as 20%, 30%, and 40%, respectively. They are blended in a ratio of 3 : 5 : a, yielding a solution with a concentration of 30%. What is the value of 'a'?Solution
Let the quantities of acids A, B, and C be 3, 5, and a units respectively. Total volume = 3+5+a=8+a. Total acid =A: 0.2×3=0.6 B: 0.3×5=1.5 C: 0.4×a=0.4a Total acid = 0.6+1.5+0.4a=2.1+0.4a Given final concentration is 30%, so: (2.1+0.4a)/(8 + a) =0.3 Multiply both sides: 2.1+0.4a = 0.3(8+a) =2.4+0.3a 0.4a − 0.3a = 2.4−2.1 ⇒0.1a=0.3 ⇒a=3
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