The strength of an indigo solution in percentage is equal to the amount of indigo in grams per $100 \mathrm{cc}$ of water. Two $800 \mathrm{cc}$ 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

Entered answer:

✅ Correct Answer: 200

Strength = grams of indigo per 100cc of water. So 33% strength means 33 grams of indigo in every 100cc of solution.

We start with two 800cc bottles: one with 33% strength, another with 17% strength. We throw away some solution from the first bottle and replace it with the same volume from the second bottle. The first bottle's strength changes from 33% to 21%. We need to find how much solution is left in the second bottle.

First bottle (33% strength):

Indigo content = 33% of 800cc = $\frac{33}{100} \times 800 = 264$ grams

Second bottle (17% strength):

Indigo content = 17% of 800cc = $\frac{17}{100} \times 800 = 136$ grams

After mixing, the first bottle has 21% strength:

Final indigo content = 21% of 800cc = $\frac{21}{100} \times 800 = 168$ grams

The first bottle lost indigo because we replaced strong solution (33%) with weaker solution (17%).

Net reduction in indigo = 264 - 168 = 96 grams

We say x cc was transferred from the second bottle to the first bottle.

When we transfer x cc:

Indigo removed from first bottle = $\frac{33}{100} \times x = 0.33x$ grams

Indigo added to first bottle = $\frac{17}{100} \times x = 0.17x$ grams

Net reduction in indigo = Indigo removed - Indigo added

$= 0.33x - 0.17x = 0.16x$ grams

Since we know the net reduction is 96 grams:

$0.16x = 96$

$x = \frac{96}{0.16} = 600$ cc

Volume transferred from second bottle = 600cc

Solution left in second bottle = 800 - 600 = 200cc

Therefore, the volume of solution left in the second bottle is 200cc.

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