Question:medium

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

Updated On: Jan 15, 2026
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Solution and Explanation

The problem is analyzed in sequential steps.

Step 1: Indigo Content in the Initial Bottle

Let \( x \) cc of solution be removed from the first bottle. The quantity of indigo in the removed portion is \( 0.33x \) grams. Following this removal, the first bottle contains \( 800 - x \) cc of solution, with \( 0.33(800) - 0.33x = 264 - 0.33x \) grams of indigo.

Step 2: Incorporating Solution from the Second Bottle

Subsequently, \( x \) cc of solution from the second bottle is added to the first. The indigo introduced from the second bottle amounts to \( 0.17x \) grams. After this addition, the total volume in the first bottle remains 800 cc. The aggregated amount of indigo in the first bottle is now \( 264 - 0.33x + 0.17x = 264 - 0.16x \) grams.

Step 3: Establishing the Mathematical Relationship

The problem states that the concentration of the solution in the first bottle becomes 21% post-operations. This implies that 800 cc of the solution contains \( 0.21 \times 800 = 168 \) grams of indigo. An equation is formulated based on this information: \[ 264 - 0.16x = 168 \] The equation is simplified as follows: \[ -0.16x = -96 \] The value of \( x \) is determined by solving for it: \[ x = \frac{-96}{-0.16} = 600 \]

Step 4: Calculating the Remaining Volume in the Second Bottle

The volume of solution retained in the second bottle is computed as: \[ \text{Initial volume} - \text{Volume extracted} = 800 \, \text{cc} - 600 \, \text{cc} = 200 \, \text{cc}. \]

Final Result:

The quantity of solution remaining in the second bottle is \( \boxed{200} \, \text{cc} \).

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