The initial ratio of sugar and flour in recipe was 17 : 28. With 27 kg of the recipe, Sunita added more flour to make the sugar to flour ratio 2:5. How much flour did Sunita later add ?

Options

A. 8.1 kg
B. 8.5 kg
C. 8.7 kg
D. 8.3 kg

Answer

To solve the problem step by step, we will follow these calculations:

1. **Understanding the Initial Ratio**:
The initial ratio of sugar to flour is given as 17:28. This means for every 17 parts of sugar, there are 28 parts of flour.

2. **Calculating the Total Parts**:
The total parts in the initial mixture can be calculated as:
\[ \text{Total parts} = 17 + 28 = 45 \]

3. **Finding the Quantity of Sugar in the 27 kg Mixture**:
We know the total weight of the mixture is 27 kg. To find the quantity of sugar, we can use the ratio:
\[ \text{Quantity of Sugar} = \left(\frac{17}{45}\right) \times 27 = \frac{17 \times 27}{45} \]
Simplifying this:
\[ \text{Quantity of Sugar} = \frac{459}{45} = 10.2 \text{ kg} \]

4. **Finding the Quantity of Flour in the 27 kg Mixture**:
Now, we can find the quantity of flour:
\[ \text{Quantity of Flour} = 27 - \text{Quantity of Sugar} = 27 - 10.2 = 16.8 \text{ kg} \]

5. **Setting Up the New Ratio**:
Sunita adds more flour to change the sugar to flour ratio to 2:5. We know the quantity of sugar remains the same (10.2 kg). Let \( x \) be the amount of flour added. The new quantity of flour will be:
\[ \text{New Quantity of Flour} = 16.8 + x \]

6. **Using the New Ratio**:
According to the new ratio of sugar to flour (2:5), we can set up the equation:
\[ \frac{10.2}{16.8 + x} = \frac{2}{5} \]

7. **Cross-Multiplying to Solve for x**:
Cross-multiplying gives us:
\[ 10.2 \times 5 = 2 \times (16.8 + x) \]
Simplifying this:
\[ 51 = 33.6 + 2x \]
Rearranging gives:
\[ 2x = 51 - 33.6 = 17.4 \]
Thus, we find:
\[ x = \frac{17.4}{2} = 8.7 \text{ kg} \]

8. **Conclusion**:
Therefore, the amount of flour Sunita added is **8.7 kg**.