A jar full of syrup solution contains 45% sugar. A part of this solution is replaced by another solution containing 20% sugar, and the percentage of sugar becomes 30%. What part of the solution was replaced?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{3}{5}\)
The final jar is a mixture of the part kept (old strength) and the part added (new strength); by alligation their ratio is set by the distances from the final strength.
Kept : replaced \(=(30-20):(45-30)=10:15\)
Part replaced \(\displaystyle =\frac{15}{25}=\frac{3}{5}\)
\(\frac{3}{5}\) of the solution was replaced.
Why the other options are incorrect
Option (1) \(\frac{2}{5}\) — Incorrect. Replacing \(\frac{2}{5}\) gives \(\frac{3}{5}\times45+\frac{2}{5}\times20=35\%\) sugar, not 30%.
Option (2) \(\frac{3}{10}\) — Incorrect. Replacing \(\frac{3}{10}\) gives \(\frac{7}{10}\times45+\frac{3}{10}\times20=37.5\%\) sugar, not 30%.
Option (3) \(\frac{1}{3}\) — Incorrect. Replacing \(\frac{1}{3}\) gives \(\frac{2}{3}\times45+\frac{1}{3}\times20=36\frac{2}{3}\%\) sugar, not 30%.