In what ratio must a mixture of 11% sugar strength be mixed with that of 25% sugar strength so as to get a new mixture of 13% sugar strength?

Options

A. `5 : 1`
B. `6:1`
C. `7:2`
D. `10:3`

Answer

To solve the problem of mixing two sugar solutions with different concentrations to achieve a desired concentration, we can follow these steps:

### Step 1: Define the variables
Let:
- A = amount of the 11% sugar solution
- B = amount of the 25% sugar solution

### Step 2: Set up the equation based on sugar content
We know that the total sugar from both solutions must equal the sugar in the new mixture. The sugar content can be expressed as:
- Sugar from A = 11% of A = 0.11A
- Sugar from B = 25% of B = 0.25B
- Sugar in the new mixture = 13% of (A + B) = 0.13(A + B)

### Step 3: Write the equation
From the above, we can set up the equation:
\[ 0.11A + 0.25B = 0.13(A + B) \]

### Step 4: Expand and rearrange the equation
Expanding the right side gives:
\[ 0.11A + 0.25B = 0.13A + 0.13B \]
Now, rearranging the equation to group like terms:
\[ 0.11A - 0.13A + 0.25B - 0.13B = 0 \]
This simplifies to:
\[ -0.02A + 0.12B = 0 \]

### Step 5: Solve for the ratio A:B
Rearranging gives:
\[ 0.02A = 0.12B \]
Dividing both sides by 0.02:
\[ A = 6B \]
Thus, the ratio A:B can be expressed as:
\[ \frac{A}{B} = \frac{6}{1} \]

### Conclusion
The required ratio of the 11% sugar solution to the 25% sugar solution is:
\[ \text{Ratio } A:B = 6:1 \]