400 g of apple vinegar has 40% apple juice in it. The amount of apple juice, which should be added to make it 60% in apple vinegar, is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 200 g
The apple juice now present is
\(40\%\text{ of }400 = 160\text{ g}\)
Let x g of apple juice be added. The juice becomes \(160 + x\) and the mixture \(400 + x\), and the juice must be 60% of the new mixture:
\( \displaystyle \frac{160 + x}{400 + x} = \frac{60}{100} \)
\(100(160 + x) = 60(400 + x)\)
\(16000 + 100x = 24000 + 60x\)
\(40x = 8000\)
\(x = 200\)
Shortcut: The rest of the vinegar, \(400 - 160 = 240\) g, does not change. In the new mixture it is 40%, so the new mixture weighs \(\frac{240}{0.4} = 600\) g, and \(600 - 400 = 200\) g of juice is added.