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Arithmetic I

Ratio & Partnership

ALL MODULES

CAT 2025 Lesson : Ratio & Partnership - Concepts & Cheatsheet

Note: The video for this module contains a summary of all the concepts covered in this 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.

9. Cheatsheet

1

) Ratio is the quantitative relationship or comparison of numbers. It indicates the relationship of one quantity with respect to another.

2

) A ratio of

2

numbers can be expressed as a fraction in this way ⇒

a : b = \dfrac{a}{b}

, where a is called the antecedent and b is called the consequent

3

)

a : b = ka : kb = \dfrac{a}{k} : \dfrac{b}{k}

4

) To simplify a ratio with fractions, we multiply the ratio with the LCM of the denominators

5

) For ratios with 2 terms, we can cross-multiply the numerators and denominators ⇒

\dfrac{a}{b} : \dfrac{c}{d} = ad : bc

6

) If

\dfrac{a}{b} \gt \dfrac{c}{d}

, then

ad \gt bc

and if

\dfrac{a}{b} \lt \dfrac{c}{d}

, then

ad \lt bc

7

) If the ratio

\dfrac{a}{b}

is multiplied with

\dfrac{m}{n}

, then

\dfrac{am}{bn} \gt \dfrac{a}{b}

where

m \gt n

and

\dfrac{am}{bn} \lt \dfrac{a}{b}

where

m \lt n

8

) If

\dfrac{a}{b} = \dfrac{p_{1}}{q_{1}}, \dfrac{b}{c} = \dfrac{p_{2}}{q_{2}}, \dfrac{c}{d} = \dfrac{p_{3}}{q_{3}}, \dfrac{d}{e} = \dfrac{p_{4}}{q_{4}}

, then

a : b : c : d : e = p_{1}p_{2}p_{3}p_{4} : q_{1}p_{2}p_{3}p_{4} : q_{1}q_{2}p_{3}p_{4} : q_{1}q_{2}q_{3}p_{4} : q_{1}q_{2}q_{3}q_{4}

9

) The quantities linked through a ratio can be represented with only 1 variable.

10

) When

a \times b = c

, and if ratio of

a

-values and

b

-values are given, then to find the ratio of the

c

-values, we can directly multiply the corresponding

a

-terms and

b

-terms in the respective ratios.

11

) For

2

partners A and B,

\dfrac{\text{Profit of A}}{\text{Profit of B}} = \dfrac{\text{Investment of A} \times \text{Duration of A's Investment}}{\text{Investment of B} \times \text{Duration of B's Investment}}

12

) Where

\text{I}_{\text{X}}

is the investment of partner X,

\text{D}_{\text{X}}

is the duration of X's investment and

\text{P}_{\text{X}}

is the Profit of partner X, the ratio of profits of

4

partners A, B, C and D is

\text{P}_{\text{A}} : \text{P}_{\text{B}} : \text{P}_{\text{C}} : \text{P}_{\text{D}} = \text{I}_{\text{A}}\text{D}_{\text{A}} : \text{I}_{\text{B}}\text{D}_{\text{B}} : \text{I}_{\text{C}}\text{D}_{\text{C}} : \text{I}_{\text{D}}\text{D}_{\text{D}}

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