Question

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Answer 1

1.
12 liters of 26% acid solution contain $26\% \times 12=0.26 \times 12=3.12$ liters of acid.
x liters of 40% acid solution contain $40\%x=0.4x$ liters of acid.
The third solution is made from the two mixed solution so its volume is $12+x$, and the volume of acid in it is $0.4x+3.12$. Its concentration is 33% or 0.33.
The concentration of a solution is the volume of the solution divide by the volume of acid in it.

$\frac{0.4x+3.12}{12+x}=0.33 \\ 0.4x+3.12=0.33(12+x) \\ 0.4x+3.12=3.96+0.33x \\ 0.07x=0.84 \\ x=12$

The answer is B.

2.
12 liters of 16% acid solution contain $16\% \times 12=0.16 \times 12=1.92$ liters of acid.
x liters of 40% acid solution contain $40\%x=0.4x$ liters of acid.
The volume of the third solution is $12+x$, and the volume of acid in it is $0.4x+1.92$. Its concentration is 32% or 0.32.

$\frac{0.4x+1.92}{12+x}=0.32 \\ 0.4x+1.92=0.32(12+x) \\ 0.4x+1.92=3.84+0.32x \\ 0.08x=1.92 \\ x=24$

The answer is B.

3.
16 liters of 18% acidsolution contain $18\% \times 16=0.18 \times 16=2.88$ liters of acid.
x liters of 27% acid solution contain $27\%x=0.27x$ liters of acid.
The volume of the third solution is $16+x$, and the volume of acid in it is $0.27x+2.88$. Its concentration is 21% or 0.21.

$\frac{0.27x+2.88}{16+x}=0.21 \\ 0.27x+2.88=0.21(16+x) \\ 0.27x+2.88=3.36+0.21x \\ 0.06x=0.48 \\ x=8$

The answer is A.