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 contains lemon juice and sugar syrup in equal proportion. A new mixture is formed by mixing the initial mixture with pure sugar syrup in the ratio 1:3. Find the final ratio of lemon juice to sugar syrup in the new mixture.

Step 1: Initial Mixture Composition

Since the mixture contains lemon juice and sugar syrup in equal proportions: \[ \text{Lemon Juice} = \frac{1}{2}, \quad \text{Sugar Syrup} = \frac{1}{2} \]

Step 2: Creating the New Mixture

The new mixture combines:

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

Total parts = \( 1 + 3 = 4 \)

 

Step 3: Sugar Syrup in the New Mixture

Sugar syrup from initial mixture: \[ \frac{1}{2} \times 1 = \frac{1}{2} \] Sugar syrup from 3 parts of pure syrup: \[ 1 \times 3 = 3 \] Total sugar syrup: \[ \frac{1}{2} + 3 = \frac{7}{2} \]

Step 4: Lemon Juice in the New Mixture

Lemon juice comes only from the initial mixture: \[ \frac{1}{2} \times 1 = \frac{1}{2} \]

Step 5: Final Ratio

Lemon Juice : Sugar Syrup = \[ \frac{1}{2} : \frac{7}{2} \Rightarrow 1 : 7 \quad (\text{after multiplying both terms by 2}) \]

Final Answer:

\[ \boxed{1 : 7} \]

Correct Option: (D)

Answer 2

An initial mixture has lemon juice and sugar syrup in the ratio \( 1:1 \). It is mixed with pure sugar syrup in the ratio \( 1:3 \). Find the final ratio of lemon juice to sugar syrup in the new mixture.

Step 1: Understand the Initial Proportions

• Lemon juice = \( 50\% \)
• Sugar syrup = \( 50\% \)

Pure sugar syrup contains \( 100\% \) sugar syrup.

Step 2: Total Parts in New Mixture

\[ \text{Total parts} = 1 + 3 = 4 \]

Step 3: Lemon Juice in New Mixture

Only the initial 1 part contains lemon juice: \[ \text{Lemon Juice} = 50\% \times \frac{1}{4} = \frac{50\%}{4} \]

Step 4: Sugar Syrup in New Mixture

• From initial mixture: \( 50\% \times \frac{1}{4} = \frac{50\%}{4} \)
• From pure syrup: \( 100\% \times \frac{3}{4} = \frac{300\%}{4} \)

Total sugar syrup: \[ \frac{50\%}{4} + \frac{300\%}{4} = \frac{350\%}{4} \]

Step 5: Final Ratio

\[ \text{Lemon Juice} : \text{Sugar Syrup} = \frac{50}{4} : \frac{350}{4} = 50 : 350 = \boxed{1 : 7} \]

Final Answer:

\[ \boxed{1 : 7} \]

Correct Option: (D)