The ratio in which two sugar solutions of the concentrations 15% and 40% are to be mixed to get a solution of concentration 30% in

Options

A. `2:3`
B. `3:2`
C. `8:9`
D. `9:8`

Answer

To find the ratio in which two sugar solutions of concentrations 15% and 40% should be mixed to obtain a solution of concentration 30%, we can use the method of alligation.

### Step-by-step Solution:

1. **Identify the Concentrations**:
- Let the concentration of the first solution (C1) = 15%
- Let the concentration of the second solution (C2) = 40%
- Let the desired concentration of the mixture (C) = 30%

2. **Apply the Alligation Method**:
- We will calculate the differences between the concentrations:
- Difference between C2 and C (40% - 30%) = 10%
- Difference between C and C1 (30% - 15%) = 15%

3. **Set Up the Ratio**:
- The ratio of the two solutions can be set up as the inverse of the differences calculated:
- The ratio of the first solution (15%) to the second solution (40%) is given by the differences:
- Ratio = Difference of C2 and C : Difference of C and C1
- Ratio = 10% : 15%

4. **Simplify the Ratio**:
- To simplify the ratio, we can divide both parts by 5:
- 10% ÷ 5 = 2
- 15% ÷ 5 = 3
- Therefore, the ratio of the two solutions is 2 : 3.

5. **Conclusion**:
- The required ratio in which the two sugar solutions should be mixed is **2 : 3**.