A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1:3, then the ratio of lemon juice and sugar syrup in the new mixture is:

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Accepted Answer

The given problem involves mixing a solution of lemon juice and sugar syrup (in equal proportions) with pure sugar syrup in the ratio 1:3. Here's the step-by-step solution:

1. **Initial Mixture Composition:**  
   The first mixture contains equal parts of lemon juice and sugar syrup, i.e., 50% lemon juice and 50% sugar syrup.

2. **Mixing Ratio:**  
   This mixture is combined with pure sugar syrup in the ratio 1:3.

3. **Sugar Syrup Concentration in New Mixture:**  
   Using weighted averages, the concentration of sugar syrup in the new mixture is:  
   $$
   	ext{Concentration} = \frac{\left(\frac{1}{2} 	imes 1ight) + (1 	imes 3)}{1 + 3} = \frac{\frac{1}{2} + 3}{4} = \frac{7}{8}.
   $$

This means that out of every 8 units of the new mixture, **7 units are sugar syrup**.

4. **Lemon Juice Proportion:**  
   Since only the initial mixture contributes lemon juice, and it was mixed in the ratio 1:3, the remaining **1 unit** (out of 8) is lemon juice.

5. **Final Ratio:**  
   The ratio of lemon juice to sugar syrup in the new mixture is:  
   $$
   	ext{Ratio} = 1 : 7.
   $$

Thus, the correct answer is **D. 1:7**.

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