Profit, Loss, Discount and Marked Price | Banking Quant Mastery

Why This Chapter Matters

Profit and loss questions test whether you can move between cost price, marked price, selling price, discount, and percentage comparison without breaking the base. Many exam traps are really just base mistakes.

Core Ideas

Profit percent is measured on cost price: $Profit% = \frac{Profit}{CP} \times 100$ .
Discount percent is measured on marked price, not cost price.
Equal profit and equal loss percentages on two items do not cancel each other when selling prices are the same. That case always creates a net loss.
When two trades happen together, calculate the total rupee effect before announcing the net percentage.
Markup and discount are chained multipliers, not subtract-and-done shortcuts.
False-weight questions are just hidden profit questions in measurement form.

High-Value Formulas

Concept	Formula / Rule
Selling price at profit	$SP = CP (1 + \frac{p}{100})$
Selling price at loss	$SP = CP (1 - \frac{l}{100})$
Selling price after discount	$SP = MP (1 - \frac{d}{100})$
Successive discount	$net discount = x + y - \frac{x y}{100}$
Equal gain-loss shortcut	$net loss % = \frac{x ^{2}}{100}$

How To Approach Questions

Identify whether the percentage is applied on CP or MP.
For markup-plus-discount questions, convert each step into a multiplier.
For overall gain/loss, add actual rupee profits and losses first.
If two items are compared together, use a common cost or common selling price before deciding the net effect.

Worked Examples

Example 1

Prompt: An article is sold for $Rs 960$ at a profit of $20%$ . Find the cost price.

Approach: If SP is $120%$ of CP, then $CP = 960 \div 1.2 = 800$ .

Example 2

Prompt: A marked price is $Rs 800$ and the discount is $10%$ . Find the selling price.

Approach: Selling price $= 800 \times 0.9 = 720$ .

Example 3

Prompt: A seller gives successive discounts of $50%$ and $50%$ . What is the real combined discount?

Approach: Do not add them as $100%$ . The item becomes $50%$ of marked price after the first discount and $25%$ after the second, so the true discount is $75%$ .

Example 4

Prompt: Two items are sold for the same price, one at $25%$ gain and the other at $25%$ loss. What is the result overall?

Approach: This is the standard equal-gain-equal-loss trap. Net loss $= \frac{2 5 ^{2}}{100} = 6.25%$ .

Common Mistakes

Applying a profit percentage to marked price.
Subtracting successive discounts directly from the original price without checking the second base.
Calling equal profit and loss percentages a break-even outcome.
Forgetting that false-weight gain is still profit on cost or true quantity.
Ignoring the actual price base in combined transactions.

Quick Revision

Profit and loss stays clean when the base is visible at every step: CP for gain/loss, MP for discount, and common price assumptions for comparison cases.

4. Profit, Loss, Discount and Marked Price