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Arithmetic I

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Profit & Loss
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CAT 2025 Lesson : Profit & Loss - Concepts & Cheatsheet

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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) Profit == SP - CP

⇒ ⇒ SP == CP + Profit

⇒⇒ CP == SP - Profit

2) Profit % =ProfitCP×100%=(SP−CP)CP×100%= \dfrac{\text{Profit}}{\text{CP}} \times 100 \% = \dfrac{(\text{SP} - \text{CP})}{\text{CP}} \times 100 \%

=(SPCP−1)×100%= \left(\dfrac{\text{SP}}{\text{CP}} - 1 \right) \times 100 \%

3) CP+CP×P100⇒SP=CP×(1+P100)\text{CP} + \text{CP} \times \dfrac{\text{P}}{100} ⇒ \text{SP} = \text{CP} \times \left(1 + \dfrac{\text{P}}{100} \right)

4) Where Mark-up %\% and Discount %\% are given,
∙\bullet MP = CP (1 + Mark-up%)
∙\bullet SP = MP (1 - Discount %)
∙\bullet SP = CP (1 + Mark up%) (1 - Discount%)

5) Note the following.
∙\bullet Profit/Loss %\bm{\%} is a percentage of CP.
∙\bullet Mark-up %\bm{\%} is a percentage of CP.
∙\bullet Discount %\bm{\%} is a percentage of MP.

6) When Discount and Mark up percentages equal x,

SP = CP (1−x21002)\left(1 - \dfrac{x^{2}}{100^{2}} \right).

∴Loss is x2100%\bm{\dfrac{x^{2}}{100} \%}

7) When SP of two products is the same and one is sold at a profit of x%x \% and the other at a loss of x%x \%, then the two transactions combined would have resulted in a loss of x2100%\bm{ \dfrac{x^{2}}{100} \%}

8) If SP of pp units equals CP of qq units, Profit %=(q−p)p×100%\% = \dfrac{(q - p)}p{ \times 100 \%}

9) When qq units are sold, if profit is SP of pp units, Profit %=p(q−p)×100%\% = \dfrac{p}{(q - p)} \times 100 \%

10) In questions involving fraudulent trader, who commits fraud while purchasing, write the CP per stated unit first and then write it as CP per actual unit. The same applies for SP for fraud while selling.

11) Where FC and VC are Fixed Cost and Variable Cost respectively,
Total Cost = FC + VC
Variable Margin = SP per unit - VC per unit
Profit = (Variable Margin ×\times Units Sold) - Fixed Cost

12) Break-even point is when Total Revenue = Total Cost.

Break-even volume =Fixed CostVariable Margin= \dfrac{\text{Fixed Cost}}{\text{Variable Margin}}

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