CAT 2022Slot 1QAQuestion & Solution
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
Options
1 : 4
1 : 5
1 : 6
1 : 7
Solution
1. Concept Used
- Topic: Mixtures and Alligations — Successive Mixing
- Formula: $$\text{Component in new mixture} = \frac{\text{(Parts of solution A)} \times \text{(Fraction of component in A)} + \text{(Parts of solution B)} \times \text{(Fraction of component in B)}}{\text{Total Parts}}$$
2. Calculation
The original mixture contains lemon juice and sugar syrup in equal proportion, i.e., 1 : 1. This means lemon juice constitutes (\frac{1}{2}) of the mixture and sugar syrup constitutes (\frac{1}{2}) of the mixture.
Pure sugar syrup contains 100% sugar syrup and 0% lemon juice.
The new mixture is formed by combining the original mixture and pure sugar syrup in the ratio 1 : 3. So assume we take 1 part of the original mixture and 3 parts of pure sugar syrup, giving a total of 4 parts.
Lemon juice in the new mixture:
$$\text{Lemon juice} = 1 \times \frac{1}{2} + 3 \times 0 = \frac{1}{2}$$
Sugar syrup in the new mixture:
$$\text{Sugar syrup} = 1 \times \frac{1}{2} + 3 \times 1 = \frac{1}{2} + 3 = \frac{7}{2}$$
Ratio of lemon juice to sugar syrup:
$$\text{Ratio} = \frac{1}{2} : \frac{7}{2} = 1 : 7$$
3. Solution
Answer = Option D ✅
The ratio of lemon juice to sugar syrup in the new mixture is 1 : 7.