Question

The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is

Accepted Answer

200. Let $V$ cc be the volume taken from the second bottle and mixed into the first bottle (after throwing away $V$ cc from the first bottle). Resulting concentration in the first bottle is $21\%$. By alligation / weighted average: $$33\%(800 - V) + 17\%(V) = 21\%(800)$$ $$33(800 - V) + 17V = 21 	imes 800$$ $$26400 - 33V + 17V = 16800$$ $$16V = 9600 \implies V = 600$$ Since $600	ext{ cc}$ was taken from the second bottle, the volume left in the second bottle is: $$800 - 600 = 200	ext{ cc}$$.

Indigo Solution Replacement

Explanation

Practise this under exam conditions