CAT 2025 Lesson : Mixtures & Alligations - Concepts & Cheatsheet

Note: The video for this module contains a summary of all the concepts covered in the Mixtures & Alligations lesson. The video would serve as a good revision. Please watch this video in intervals of a few weeks so that you do not forget the concepts. Below is a cheatsheet that includes all the formulae but not necessarily the concepts covered in the video.

8. Cheatsheet

1)

x_{4} = \dfrac{x_{1}w_{1} + x_{2}w_{2} + ... + x_{n}w_{n}}{w_{1} + w_{2} + ... + w_{n}}

2)

\dfrac{w_{1}}{w_{2}} = \dfrac{(x_{2} - x_{A})}{(x_{A} - x_{2})}

3

) Where $\bm{I}$ is the initial quantity of non-replaced liquid,
$\bm{r\%}$ is the replacement percentage,
$\bm{n}$ is the number of replacements,
$\bm{F}$ is the final quantity of the non-replaced liquid,

F = I \times \left(1 - \dfrac{r}{100} \right)^{n}

4

) If the quantity replaced is provided (for example, in litres) instead of percentage,

F = I \times \left(1 - \dfrac{\text{Replacement Quantity}}{\text{Total Quantity}} \right)^{n}

5

) Where the quantities of

2

mixtures of different unknown concentrations are $\bm{a}$ and $\bm{b}$ , and a quantity of $\bm{x}$ is removed from each of the mixtures and placed in the other mixtures, and this results in both the mixtures having the same concentrations, then

x = \dfrac{ab}{a + b}

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