Profit and Loss: Formulas, Shortcuts, and Worked Examples

Profit and loss questions appear in every major placement aptitude test (TCS NQT, AMCAT, Cocubes), and the entire topic reduces to eight core formulas and a handful of shortcuts.

Core Terms You Need Before the Formulas

Get these definitions solid before touching the formula table. Confusion between CP and SP, or between discount percentage and profit percentage, is responsible for most wrong answers in this topic.

• Cost Price (CP): The price at which an item is purchased. All profit and loss percentages are calculated relative to CP, not to SP.
• Selling Price (SP): The price at which an item is sold.
• Profit: Occurs when SP exceeds CP. Profit = SP - CP.
• Loss: Occurs when CP exceeds SP. Loss = CP - SP.
• Profit Percentage: (Profit / CP) × 100. Always divide by CP.
• Loss Percentage: (Loss / CP) × 100. Always divide by CP.
• Marked Price (MP): The price displayed on the product tag, before any discount is applied.
• Discount: The reduction given on the Marked Price. Discount = MP - SP.
• Discount Percentage: (Discount / MP) × 100. Note: discount percentage uses MP as the base, not CP.

One exam trap worth flagging before the formulas: profit percentage and loss percentage always use Cost Price in the denominator. When a question gives you the Selling Price and asks for the CP, that requires the reverse formula rather than on-the-spot algebra.

The 8 Formulas That Cover the Syllabus

Every profit and loss question in placement aptitude tests traces to one of these eight relationships. Learn them as a set; the pattern becomes clear when you see all eight together.

Relationship	Formula
Profit	SP - CP
Loss	CP - SP
Profit %	(Profit / CP) × 100
Loss %	(Loss / CP) × 100
SP when profit% is known	((100 + P%) / 100) × CP
SP when loss% is known	((100 - L%) / 100) × CP
CP when profit% and SP are known	(100 / (100 + P%)) × SP
CP when loss% and SP are known	(100 / (100 - L%)) × SP

The bottom two rows are where most marks are lost. Exam questions frequently state the SP and a profit or loss percentage, then ask for the CP. Apply the CP-finding formula directly from the table rather than rearranging during the test.

Two practical notes. First, if the question uses gain instead of profit, they mean the same thing; the terms are interchangeable in aptitude. Second, all four percentage formulas follow the same structure: numerator is the change, denominator is the reference base, multiplied by 100. Profit% and loss% reference CP. Discount% references MP.

Three Shortcuts for Exam Conditions

Successive Discounts

When two discounts are applied one after the other, the final selling price reflects a compound reduction, not a simple sum of the percentages.

• Formula: Combined Discount% = a + b - (a × b / 100)
• Example: Successive discounts of 30% and 20%.
  • Combined% = 30 + 20 - (30 × 20 / 100) = 50 - 6 = 44%
  • Adding the discounts directly gives 50%, which is wrong.
• Verification on ₹1,000 marked price: After 30% discount → ₹700. After 20% discount on ₹700 → ₹560. Total discount = ₹440 = 44% of ₹1,000. The formula is confirmed.

The reason the combined discount is always less than the arithmetic sum: the second discount applies to a base already reduced by the first discount, not to the original marked price.

If Selling Price Is Doubled and Profit Triples

This pattern gives a conditional relationship between profit and SP and asks for the original profit percentage. It needs equation setup, not a stored formula.

• Let CP = x, original SP = y. Original profit = y - x.
• When SP doubles to 2y, profit triples: 3(y - x) = 2y - x.
• Expanding: 3y - 3x = 2y - x, which gives y = 2x.
• Original profit% = (y - x) / x × 100 = (2x - x) / x × 100 = 100%.

The pattern repeats in various forms: profit doubles when SP increases by a certain percentage, and so on. In all cases, assign CP and SP as variables, write the equation for the new condition, and solve.

False Weights

A trader uses an incorrect (false) weight while selling goods. The customer pays for a standard quantity but receives less. The trader earns a gain even when selling at cost price.

• Formula: Gain% = Error / (True Weight - Error) × 100
• Example: Trader uses 900g instead of 1 kg.
  • Error = 1,000 - 900 = 100g
  • Gain% = 100 / (1,000 - 100) × 100 = 100 / 900 × 100 = 11.11%
• Alternative form: If the error is expressed as x% of the true weight, use Gain% = x / (100 - x) × 100. For the example above, x = 10, so Gain% = 10 / 90 × 100 = 11.11%.

Five Worked Examples

Work through each one before reading the answer. The structure of each solution matters as much as the final number.

Example 1: Basic Profit Percentage

• A shopkeeper buys goods at ₹400 and sells them at ₹500.
• Profit = 500 - 400 = ₹100.
• Profit% = (100 / 400) × 100 = 25%.

Example 2: Finding SP from Profit Percentage

• CP = ₹800. The item is sold at 15% profit. Find the Selling Price.
• SP = ((100 + 15) / 100) × 800 = (115 / 100) × 800 = ₹920.

Example 3: Finding CP from SP and Profit Percentage

• A shirt is sold at ₹480 at 20% profit. Find the Cost Price.
• CP = (100 / (100 + 20)) × 480 = (100 / 120) × 480 = ₹400.
• Sanity check: profit on ₹400 at 20% = ₹80. SP = 400 + 80 = ₹480. ✓

Example 4: Successive Discounts

• Marked price of a jacket is ₹1,000. Discounts of 30% then 20% are applied.
• Combined discount% = 30 + 20 - (30 × 20 / 100) = 44%.
• SP = 1,000 × (1 - 44/100) = 1,000 × 0.56 = ₹560.

Example 5: False Weight

• A trader uses a 900g weight when selling rice at its cost price per kg.
• Error = 1,000 - 900 = 100g.
• Gain% = 100 / (1,000 - 100) × 100 = 100 / 900 × 100 = 11.11%.

How Profit and Loss Appears in Placement Tests

Profit and loss is a core component of the numerical ability section in AMCAT’s quantitative module and in standard campus placement evaluation tests. The five question types covered in this guide (basic profit/loss calculation, finding CP or SP from the other plus a percentage, marked price and discount, successive discounts, and false weights) cover the broad majority of what appears in actual aptitude tests.

The best books for placement preparation treat profit and loss as a multi-chapter topic, but the exam reality is simpler than the chapter count suggests. Work through IndiaBix profit and loss practice problems across all five types. By the time you have seen 20 problems per type, the structure becomes automatic and exam-time pressure stops affecting accuracy. Time and work questions sit in the same numerical ability section and follow the same preparation logic: learn the core method, then drill variants.

The eight formulas in this guide reduce an entire placement aptitude topic to a single reference table. Once profit and loss is solid, the remaining gap in most engineers’ placement preparation is demonstrating any AI-adjacent skill to recruiters who now ask for it in technical rounds. TinkerLLM (₹499) is a hands-on environment where you write prompts, inspect outputs, and see what changes when parameters shift. It’s not a video series; the skill comes from building, not watching.