Question

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

• A. 1:6
• B. 1:4
• C. 1:5
• D. 1:7

Answer 1

The Correct Option is D

An initial mixture comprises equal parts of lemon juice and sugar syrup. A new mixture is formulated by combining the initial mixture with pure sugar syrup in a 1:3 ratio. Determine the final ratio of lemon juice to sugar syrup in the new mixture.

Step 1: Initial Mixture Composition

Given that the initial mixture contains lemon juice and sugar syrup in equal proportions:

\[ \text{Lemon Juice Proportion} = \frac{1}{2}, \quad \text{Sugar Syrup Proportion} = \frac{1}{2} \]

Step 2: Formation of the New Mixture

The new mixture is created by combining:

• 1 part of the initial mixture
• 3 parts of pure sugar syrup

The total number of parts in the new mixture is \( 1 + 3 = 4 \).

Step 3: Quantifying Sugar Syrup in the New Mixture

Sugar syrup contributed by the initial mixture is \( \frac{1}{2} \times 1 = \frac{1}{2} \).

Sugar syrup contributed by the pure sugar syrup is \( 1 \times 3 = 3 \).

The total amount of sugar syrup in the new mixture is \( \frac{1}{2} + 3 = \frac{7}{2} \).

Step 4: Quantifying Lemon Juice in the New Mixture

Lemon juice is exclusively derived from the initial mixture. The amount of lemon juice is \( \frac{1}{2} \times 1 = \frac{1}{2} \).

Step 5: Determining the Final Ratio

The ratio of Lemon Juice to Sugar Syrup in the new mixture is:

\[ \frac{1}{2} : \frac{7}{2} \]

Multiplying both terms by 2 to simplify yields a ratio of \( 1 : 7 \).

Final Answer:

\[ \boxed{1 : 7} \]

Correct Option: (D)