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

Answer 1

Correct Answer: 200

Step 1: Removing Solution from the First Bottle

Suppose \( x \) cc of the solution from the first bottle is thrown away. The amount of indigo in the solution that is thrown away is:

\[ \text{Amount of indigo thrown away} = 0.33x \, \text{grams}. \]

After this, the amount of solution left in the first bottle is \( 800 - x \) cc, and the amount of indigo left in the first bottle is:

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

Step 2: Adding Solution from the Second Bottle

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

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

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

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

Step 3: Using the Strength of the Solution

It's given that after these operations, the strength of the solution in the first bottle changes to 21%. So, the amount of indigo in 800 cc of the solution is:

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

Setting up the equation from the above information:

\[ 264 - 0.16x = 168. \]

Step 4: Solving the Equation

Now, solving the equation:

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

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

Step 5: Finding the Volume Left in the Second Bottle

So, \( 600 \) cc of the solution was taken from the second bottle.

Now, to find the volume of the solution left in the second bottle:

\[ \text{Original volume} - \text{Volume taken out} = 800 \, \text{cc} - 600 \, \text{cc} = 200 \, \text{cc}. \]

Conclusion

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