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CAT 2022 Slot 1 — QA Question 11

MixturesEasy

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

Answer & solution

Correct answer: 1 : 7

  • A

    1 : 4

  • B

    1 : 6

  • C

    1 : 5

  • 1 : 7

Solution

Easy

Pick a convenient amount of the first mixture, split it into its lemon and sugar parts, then dump in the extra sugar syrup. Counting actual units beats juggling ratios.

1

Choose easy quantities. Take 1010 units of the original mixture mixed with sugar syrup in the ratio 1:31:3, so 3030 units of syrup are added:

mixture:syrup=1:3 ⇒ 10 units:30 units\text{mixture}:\text{syrup}=1:3\ \Rightarrow\ 10\ \text{units}:30\ \text{units}
2

Break up the original mixture. It holds lemon juice and sugar syrup in equal proportion, so the 1010 units split evenly:

lemon=5,syrup=5\text{lemon}=5,\qquad \text{syrup}=5
3

Total each component. The added 3030 units are pure syrup:

lemon=5syrup=5+30=35\begin{aligned} &\text{lemon}=5\\ &\text{syrup}=5+30=35 \end{aligned}
4

Form the final ratio.

lemon:syrup=5:35=1:7\text{lemon}:\text{syrup}=5:35=1:7

lemon:syrup=1:7\text{lemon}:\text{syrup}=\mathbf{1:7} — option (d).

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CAT 2022 Slot 1 QA Q11: A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this — Solution | TheCATExam