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
- 1 : 6
- 1 : 4
- 1 : 5
- 1 : 7
The Correct Option is D
Solution and Explanation
Initial Mixture Composition: The initial mixture contains lemon juice and sugar syrup in equal proportion. This means that the concentration of sugar syrup in the mixture is 1/2, and the concentration of lemon juice is also 1/2.
Creating the New Mixture: A new mixture is formed by combining the initial mixture and pure sugar syrup in a ratio of 1:3. This means that for every 1 unit of the initial mixture, 3 units of pure sugar syrup are added.
Calculating Sugar Syrup Concentration in the New Mixture: To find the concentration of sugar syrup in the new mixture, we can calculate the total concentration of sugar syrup contributed by both the initial mixture and the pure sugar syrup.
Concentration from Initial Mixture: 1/2 * 1 = 1/2
Concentration from Pure Sugar Syrup: 1 * 3 = 3
Total Concentration in the New Mixture: 1/2 + 3 = 7/2
Determining the Ratio of Lemon Juice and Sugar Syrup: Since the new mixture's concentration of sugar syrup is 7/2, the concentration of lemon juice in the new mixture must be (8 - 7/2) = 1/2. This is because the total concentration of the mixture is 8 (1 + 3 = 4 units of the initial mixture and 4 units of pure sugar syrup).
Final Ratio in the New Mixture: The ratio of lemon juice to sugar syrup in the new mixture can be expressed as 1/2 : 7/2. To simplify this ratio, we can multiply both parts by 2 to get the ratio 1 : 7.
Hence, the ratio of lemon juice to sugar syrup in the new mixture is 1 : 7.
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