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
Show Solution

Correct Answer: 200

Solution and Explanation

Step 1: Solution Removal from First Bottle

Assume \( x \) cc of solution is removed from the first bottle. The quantity of indigo removed is:

\[ \text{Indigo Removed} = 0.33x \, \text{grams}. \]

The remaining solution volume in the first bottle is \( 800 - x \) cc, and the remaining indigo is:

\[ 0.33(800) - 0.33x = 264 - 0.33x \, \text{grams}. \]

Step 2: Solution Addition from Second Bottle

Subsequently, \( x \) cc of solution from the second bottle is added to the first. The indigo introduced from the second bottle is:

\[ 0.17x \, \text{grams}. \]

After this, the total volume in the first bottle remains 800 cc. The total indigo in the first bottle is now:

\[ 264 - 0.33x + 0.17x = 264 - 0.16x \, \text{grams}. \]

Step 3: Utilizing Solution Concentration

Following these actions, the solution concentration in the first bottle becomes 21%. Therefore, the indigo content in 800 cc of the solution is:

\[ 0.21 \times 800 = 168 \, \text{grams}. \]

The equation is formulated as follows:

\[ 264 - 0.16x = 168. \]

Step 4: Equation Solution

Solving the equation:

\[ -0.16x = 168 - 264 = -96, \]

\[ x = \frac{-96}{-0.16} = 600. \]

Step 5: Remaining Volume in Second Bottle

Thus, 600 cc of solution was taken from the second bottle.

The volume of solution remaining in the second bottle is calculated as:

\[ \text{Initial Volume} - \text{Volume Removed} = 800 \, \text{cc} - 600 \, \text{cc} = 200 \, \text{cc}. \]

Conclusion

Consequently, the volume of solution remaining in the second bottle is 200 cc.

Was this answer helpful?
0

Top Questions on Mixture Problems

Questions Asked in CAT exam

The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
View Solution