At a biotechnology facility, a solution tank initially contains a mixture of ethanol, wate… — GMAT

At a biotechnology facility, a solution tank initially contains a mixture of ethanol, water, and stabilizer liquid. By volume, $0.36$ of the initial mixture is ethanol and $\frac{2}{5}$ is water, with the remainder consisting of stabilizer liquid. During a purification process, $25\%$ of the ethanol and $\frac{1}{8}$ of the water evaporate, while the volume of the stabilizer liquid remains unchanged. If the volume of the remaining stabilizer liquid is $132$ liters, by what percentage did the total volume of the liquid mixture in the tank decrease?

14%Cevap
B
16.28%
C
18.75%
D
37.50%
E
24.00%

Cevap

The total volume of the liquid mixture in the tank decreased by 14%.

The initial mixture consists of 36% ethanol, 40% water, and 24% stabilizer by volume. Ethanol loses 25% of its volume, which corresponds to

0.25 \times 36\% = 9\%

of the total initial mixture volume. Water loses

\frac{1}{8}

of its volume, corresponding to

\frac{1}{8} \times 40\% = 5\%

of the total initial mixture volume. Combining these losses gives

9\% + 5\% = 14\%

net decrease relative to the initial total volume.

Adım Adım Çözüm

Express initial component proportions as unified decimals or fractions.

Ethanol fraction =

0.36 = \frac{9}{25}

. Water fraction =

\frac{2}{5} = 0.40 = \frac{10}{25}

. Stabilizer fraction =

1 - (0.36 + 0.40) = 0.24 = \frac{6}{25}

Establishing all initial parts relative to the total initial volume allows step-by-step proportion tracking.

Calculate the fraction of total volume lost due to evaporation for each component.

Ethanol loss =

25\% \times 0.36 = 0.25 \times 0.36 = 0.09

of initial total volume. Water loss =

\frac{1}{8} \times 0.40 = 0.125 \times 0.40 = 0.05

of initial total volume.

Applying the component-specific percentage decrease to each component's fraction yields its contribution to the overall volume loss.

Sum the component volume losses to find the total percentage decrease.

Total volume loss fraction =

0.09 + 0.05 = 0.14

, which equals

14\%

of the total initial volume.

The stabilizer experience no loss, so the net change in total volume is the direct sum of the losses in ethanol and water relative to the original base.

Anahtar Kavram

Multi-step arithmetic operations combining decimals, fractions, and weighted percent changes using a consistent base value.

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