NEOCODE

Profit and Loss - Easy Guide

Basic Terminology

Cost Price (C.P.): The price at which an item is purchased.
Selling Price (S.P.): The price at which an item is sold.
Profit/Loss: The difference between S.P. and C.P. If positive, it's profit; if negative, it's loss.
Profit/Loss %: Profit or loss expressed as a percentage of C.P.
Margin: Profit as a percentage of S.P.
Marked Price (M.P.): The price displayed on the label.
Discount: Reduction given on the marked price before selling.
Mark-up: Increment on the cost price before selling.

        Note: Mark-up price is always greater than C.P., and the percentage increase is calculated on C.P.
    

Formulas and Shortcuts

Concept	Formula
Profit	$Profit = S.P. - C.P.$
Loss	$Loss = C.P. - S.P.$
Profit %	$Profit % = \frac{Profit}{C.P.} \times 100$
Loss %	$Loss % = \frac{Loss}{C.P.} \times 100$
Selling Price (Profit)	$S.P. = C.P. \times (1 + \frac{Profit %}{100})$
Selling Price (Loss)	$S.P. = C.P. \times (1 - \frac{Loss %}{100})$
Cost Price (Profit)	$C.P. = \frac{S.P.}{1 + \frac{Profit %}{100}}$
Cost Price (Loss)	$C.P. = \frac{S.P.}{1 - \frac{Loss %}{100}}$
Discount	$Discount = M.P. - S.P.$
Discount %	$Discount % = \frac{Discount}{M.P.} \times 100$
Mark-up %	$Mark-up % = \frac{M.P. - C.P.}{C.P.} \times 100$

Examples

Example 1: If C.P. = ₹500 and S.P. = ₹600, find profit and profit %.
Solution:

Profit = S.P. - C.P. = 600 - 500 = 100

Profit % = \frac{100}{500} \times 100 = 20 %

Example 2: If C.P. = ₹800 and Loss % = 10%, find S.P.
Solution:

S.P. = C.P. \times (1 - \frac{10}{100}) = 800 \times 0.9 = 720

Tips and Tricks

Tip 1: For quick calculations, memorize the formulas for S.P. and C.P. in terms of profit and loss percentages.

Tip 2: Use the unitary method for discount-related problems. For example, if a discount of 20% is given, the selling price is 80% of the marked price.

Tip 3: For successive discounts, use the formula:

Net Discount = D_{1} + D_{2} - \frac{D_{1} \times D_{2}}{100}

Important Questions

If the cost price of an item is ₹1200 and it is sold at a profit of 15%, find the selling price.
A shopkeeper offers a discount of 25% on a marked price of ₹2000. Find the selling price.
If an item is sold at a loss of 10% for ₹900, find its cost price.