Back to Home
Back to Blog

💰 Profit & Loss: The Complete Guide

Master the Fraction Method - Solve CP, SP, Markup & Discount Problems Without Formulas! Trusted by 50,000+ IBPS, SBI, SSC aspirants!

Topic: Arithmetic Reading Time: 15 mins Updated: Dec 2024 Basic to Advanced

What is Profit & Loss?

Profit and Loss is the backbone of banking arithmetic. It appears in almost every competitive exam — IBPS PO, SBI Clerk, SSC CGL, Railway and more. Understanding the relationship between Cost Price (CP), Selling Price (SP), and Marked Price (MP) is essential!

CP
Cost Price
+Markup
MP
Marked Price
-Discount
SP
Selling Price

Why Profit & Loss is a Game-Changer?

In IBPS PO 2023, 5-7 questions came from Profit, Loss, Discount & Markup. The Fraction Method helped toppers avoid decimal calculations entirely! That's 2-3 minutes saved on just this topic!

Part 1: Basic Definitions & Formulas

Term Definition
Cost Price (CP) The price at which an item is purchased. This is your investment.
Selling Price (SP) The price at which an item is sold. This is your return.
Marked Price (MP) The price labeled on the product (before any discount).
Profit When SP > CP. Formula: Profit = SP - CP
Loss When CP > SP. Formula: Loss = CP - SP
Discount Reduction from MP. Formula: Discount = MP - SP

📐 Percentage Formulas:

📌 PROFIT & LOSS PERCENTAGE
Profit % = (Profit / CP) × 100   |   Loss % = (Loss / CP) × 100
📌 FINDING SP FROM CP
With Profit: SP = CP × (1 + P%/100)   |   With Loss: SP = CP × (1 - L%/100)
📌 DISCOUNT & MARKUP
Discount % = (Discount / MP) × 100   |   Markup % = (Markup / CP) × 100

Pro-Tip: Profit/Loss is ALWAYS on CP!

Remember: Profit% and Loss% are always calculated on Cost Price, not on Selling Price. This is the most common mistake students make!

Part 2: The Fraction Method (Exam Shortcut)

Formulas are good for school, but in exams, use the Fraction Method to avoid decimal calculations entirely!

📐 Step 1: Memorize Percent-to-Fraction Conversions

10%
1/10
12.5%
1/8
20%
1/5
25%
1/4
33.33%
1/3
50%
1/2
1

Convert Percentage to Fraction

20% Profit = 1/5. Here, denominator (5) = CP units, numerator (1) = Profit units.

2

Calculate SP Units

For Profit: SP = CP + Profit = 5 + 1 = 6 units
For Loss: SP = CP - Loss = 5 - 1 = 4 units

3

Set Up the Equation

Given value (SP or CP) = X units. Find what 1 unit equals.

4

Multiply to Get Answer

Required value = Required units × Value of 1 unit. Done!

Solved Example 1: Find CP from SP

Question: A shopkeeper sells an item for ₹630 at 12.5% Profit. Find CP.

Solution using Fraction Method:

• 12.5% = 1/8
• CP = 8 units, Profit = 1 unit
• SP = 8 + 1 = 9 units
• Given: SP = ₹630 = 9 units
• 1 unit = 630/9 = ₹70
• CP = 8 units = 8 × 70 = ₹560

Answer: CP = ₹560

Solved Example 2: Find SP with Loss

Question: An item bought for ₹400 is sold at 25% loss. Find SP.

Solution:

• 25% = 1/4
• CP = 4 units, Loss = 1 unit
• SP = 4 - 1 = 3 units
• Given: CP = ₹400 = 4 units
• 1 unit = 400/4 = ₹100
• SP = 3 units = 3 × 100 = ₹300

Answer: SP = ₹300

Part 3: Special Cases & Tricky Formulas

1 Two Articles Sold at Same SP (One Profit, One Loss)

If two articles are sold at the same selling price, one at x% profit and other at x% loss:

📌 ALWAYS RESULTS IN LOSS!
Net Loss % = (x / 10)² %   OR   Net Loss % = (x² / 100) %
Solved Example 3

Question: Two articles sold at ₹500 each. One at 20% profit, one at 20% loss. Find net result.

Solution:
• Loss % = (20/10)² = 2² = 4% Loss

Answer: 4% Net Loss (regardless of SP value!)

2 Dishonest Shopkeeper (Faulty Weights)

If a shopkeeper marks up by x% and also cheats on weight by y%:

📌 DISHONEST SHOPKEEPER FORMULA
Overall Gain % = [(Markup + Weight Cheat) / (100 - Weight Cheat)] × 100
Solved Example 4

Question: A shopkeeper claims to sell at cost price but uses 900g weight instead of 1kg. Find gain%.

Solution:
• Markup = 0% (selling at CP), Weight cheat = 10% (100g less)
• Gain = (0 + 10) / (100 - 10) × 100
• Gain = 10/90 × 100 = 11.11%

Answer: 11.11% Profit

3 Successive Discounts

When multiple discounts are given one after another:

📌 TWO SUCCESSIVE DISCOUNTS a% and b%
Equivalent Discount = a + b - (a×b/100) %
Solved Example 5

Question: Find equivalent discount for 20% and 10% successive discounts.

Solution:
• Equivalent = 20 + 10 - (20×10/100)
• Equivalent = 30 - 2 = 28%

Answer: 28% Equivalent Discount

5 Pro-Tips to Master Profit & Loss

Tip 1: Memorize Fraction Conversions

Must-know fractions:
10% = 1/10, 12.5% = 1/8, 16.67% = 1/6, 20% = 1/5, 25% = 1/4, 33.33% = 1/3, 50% = 1/2

Tip 2: Profit/Loss Always on CP

Never calculate profit/loss percentage on SP! The base is always Cost Price.

Tip 3: Discount Always on MP

Discount percentage is calculated on Marked Price, not on CP or SP.

Tip 4: Use the Chain Rule

CP → (1 + Markup%) → MP → (1 - Discount%) → SP → Compare with CP for Profit/Loss

Tip 5: Practice 30 Questions Daily

Profit-Loss becomes intuitive after consistent practice. Aim for 30 questions for 5 days!

Frequently Asked Questions (FAQ)

Q1: What is the difference between CP, SP, and MP?
CP (Cost Price) is the purchase price. SP (Selling Price) is the price at which you sell. MP (Marked Price) is the label price before any discount. The flow is: CP → (+Markup) → MP → (-Discount) → SP.
Q2: What is the Fraction Method?
The Fraction Method converts percentages to fractions (e.g., 20% = 1/5). The denominator represents CP. For 20% profit: CP=5 units, Profit=1 unit, SP=6 units. This avoids decimal calculations entirely!
Q3: How many Profit-Loss questions come in Bank exams?
In IBPS PO/Clerk, SBI PO/Clerk: 4-6 questions (combined with Discount & Markup). In SSC CGL/CHSL: 2-4 questions. This is one of the highest weightage topics in Quant!
Q4: When selling at same SP with equal profit & loss %, is there net profit?
No! There is always a net LOSS. The formula is: Net Loss % = (x/10)² where x is the profit/loss percentage. This is a classic trap question in exams!
Q5: How do successive discounts work?
Successive discounts are not additive. For discounts a% and b%: Equivalent = a + b - (ab/100). Example: 20% and 10% = 28% (not 30%)! The second discount applies on the already reduced price.

Quick Reference Cheat Sheet

📐 Profit %

P% = (P/CP) × 100

📉 Loss %

L% = (L/CP) × 100

🏷️ Discount %

D% = (D/MP) × 100

⚖️ Same SP Trap

Loss = (x/10)²%

🚀 Ready to Practice?

Ab aapko Profit & Loss ki poori samajh aa gayi! Time to test your skills with real exam-level questions!

Start Practice Now →