CAT 2022 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like **Speed-time-distance**, **Mixture and Alligations**. This year, there was a surprise. The questions from **Geometry** were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 3 : 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

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The concentration of sugar syrup in the mixture is \(\frac{1}{2}\). (The mixture has equal quantities of lemon juice and sugar syrup)

The concentration of sugar syrup in pure sugar syrup is 1.

The initial mixture and the pure sugar syrup are mixed in a ratio 1 : 3 to form a new mixture.

That is 2 items with sugar syrup concentrations \(\frac{1}{2}\) and 1 respectively are mixed in the ratio 1 : 3 to form a new mixture. So the concentration of sugar syrup in such a new mixture is \(\frac{\frac{1}{2} * 1+1 * 3}{1+3}=\frac{3.5}{4}=\frac{7}{8}\)

The concentration of sugar syrup in the new mixture is \(\frac{7}{8}\), that means out of 8 units of volume of the new mixture, 7 units are sugar syrup and the remaining one unit is lemon juice.

Hence the ratio of lemon juice to sugar syrup in the new mixture is 1 : 7

__Alternate Approach:__

We are mixing a mixture of lemon juice and sugar syrup with pure sugar syrup in a ratio 1 : 3.

That means, we mix 1 unit of this mixture with 3 units of pure sugar syrup.

This is equivalent to mixing 2 units of the mixture with 6 units of pure sugar syrup.

But what do we know about this mixture of lemon juice and sugar syrup?

We know that it contains equal quantities of lemon juice and sugar syrup. This means we can consider two units of this mixture as a unit each of lemon juice and sugar syrup.

Clearly, the new mixture contains one unit of lemon juice and 7 units of sugar syrup.

Hence, the ratio of lemon juice to sugar syrup in the new mixture is 1 : 7

Choice D is the correct answer.

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