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

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 \(\frac 12\), and the concentration of lemon juice is also \(\frac 12\).
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: \(\frac 12  \times1 = \frac 12\)

Concentration from Pure Sugar Syrup: \(1\times3 = 3\)

Total Concentration in the New Mixture: \(\frac 12 + 3 = \frac 72\)

Determining the Ratio of Lemon Juice and Sugar Syrup: Since the new mixture's concentration of sugar syrup is \(\frac 72\), the concentration of lemon juice in the new mixture must be \((8 - \frac 72) = \frac 12\). 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 \(\frac 12 : \frac 72\). To simplify this ratio, we can multiply both parts by 2 to get the ratio 1 : 7.

Hence, the correct option is (D): \(1 : 7.\)

Answer 2

The proportion of lemon juice to sugar syrup in the mixture is \(1:1\), this means \(50\%\) Lemon juice and \(50\%\) sugar syrup.
In sugar syrup, there is \(100\%\) sugar syrup.
Sum of the ratio \(= 1+3 = 4\)

Lemon juice \(= 50\% \times \frac 14 = \frac {50\%}{4}\)

Sugar syrup \(= 50\% \times \frac 14 + 100\% \times \frac 34 = \frac {350\%}{4}\)

Required ratio \(= \frac {50}{350} = 1:7\)

So, the correct option is (D): \(1:7\)