Profit and loss

📘 Profit, Loss, Discount & Marked Price

Basic Definitions

Cost Price (CP): Buying price
Selling Price (SP): Selling price
Marked Price (MP): Printed price
Discount: Reduction on MP

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Profit & Loss

\[ \text{Profit} = \text{SP} - \text{CP} \]

\[ \text{Loss} = \text{CP} - \text{SP} \]

\[ \text{Profit \%} = \frac{\text{Profit}}{\text{CP}} \times 100 \]

\[ \text{Loss \%} = \frac{\text{Loss}}{\text{CP}} \times 100 \]

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Discount & Marked Price

\[ \text{Discount} = \text{MP} - \text{SP} \]

\[ \text{Discount \%} = \frac{\text{Discount}}{\text{MP}} \times 100 \]

\[ \text{SP} = \text{MP}\left(1 - \frac{x}{100}\right) \]

\[ \text{MP} = \frac{\text{SP} \times 100}{100 - x} \]

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Finding Cost Price

\[ \text{SP} = \text{CP}\left(1 + \frac{x}{100}\right) \]

\[ \text{CP} = \frac{\text{SP} \times 100}{100 + x} \]

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🔥 Exam Shortcuts & Tricks

Profit Shortcut:
Profit \(x\%\) → CP : SP = \(100 : (100 + x)\)

Loss Shortcut:
Loss \(x\%\) → CP : SP = \(100 : (100 - x)\)

Discount Shortcut:
Discount \(x\%\) → MP : SP = \(100 : (100 - x)\)

Multiplier Method:
20\% profit → \(\times 1.2\)
10\% loss → \(\times 0.9\)
25\% discount → \(\times 0.75\)

Successive Discount: \[ \text{Net Discount} = a + b - \frac{ab}{100} \]

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📘 Solved Examples

Example 1:
CP = 500, SP = 650
\[ \text{Profit} = 650 - 500 = 150 \] \[ \text{Profit \%} = \frac{150}{500} \times 100 = 30\% \]

Example 2:
MP = 1000, Discount = 20\%
\[ \text{SP} = 1000 \times \left(1 - \frac{20}{100}\right) = 800 \]

Example 3:
SP = 720, Discount = 10\%
\[ \text{MP} = \frac{720 \times 100}{90} = 800 \]

Example 4 (Successive Discount):
20\% and 10\% discount
\[ \text{Net Discount} = 20 + 10 - \frac{200}{100} = 28\% \]

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