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Profit, Loss and Discount: Complete Guide, Formulas & Shortcuts for Competitive Exams

September 21, 2026 TestQuiz 7 min read 117 views Updated September 22, 2026 (9 days ago) Quantitative Analysis (Profit, Loss and Discount)

The Ultimate Guide to Profit, Loss, and Discount: From Basics to Mains Level Mastery

Welcome, math enthusiasts and exam warriors! If there is one topic in quantitative aptitude that scares people, it’s Profit, Loss, and Discount. But here’s a secret: it’s just a giant puzzle of ratios, multipliers, and logical bridges.

I’ve gone through a comprehensive set of lecture notes (from Kaushik Mohanty’s bank exam prep series) covering everything from basic definitions to Mains-level data sufficiency. Today, I’m breaking down every single concept into a human-friendly blog post.

To make this truly useful, I’m not just copying the examples from the notes. I’m changing all the numbers and scenarios to give you a fresh perspective while keeping the core concepts exactly the same. Let’s dive in!

Module 1: The Holy Trinity (CP, SP, MP)

Before we run, we need to walk. Every problem revolves around three players:

Cost Price (CP): What the shopkeeper pays to get the item.
Selling Price (SP): What the customer pays to take it home.
Marked Price (MP): The sticker price on the tag.

The Golden Rule: Profit/Loss is always calculated on CP. Discount is always calculated on MP.

The "Bridge" Concept

The Selling Price (SP) acts as the bridge between two worlds:

CP + Profit (or - Loss) = SP
MP - Discount = SP

Example: Imagine a shopkeeper buys a lamp for Rs.200. He marks it up to Rs.250. He gives a Rs.30 discount and sells it for Rs.220.

His CP = Rs.200, SP = Rs.220, MP = Rs.250.
Markup Value = Rs.50. Discount Value = Rs.30. Profit = Rs.20.

Module 2: The Foundation & The "What If" Scenarios

In basic problems, they just ask you to find the profit %. But in real exams, they love to play "What If?"

Concept 1: Overhead Costs
Never forget that transportation, repair, or maintenance costs add to your CP.

Example: Bought a machine for Rs.5,000. Spent Rs.500 on repairs. Sold for Rs.6,600.
Solution: Total CP = Rs.5,500. Profit = Rs.1,100. Profit % = (1100/5500) × 100 = 20%.

Concept 2: The "What If" Trap (Change in CP and SP)
If a shopkeeper changes his buying price and selling price, the profit % changes.

Example: A shopkeeper sold a watch at a 40% loss. If he had bought it for Rs.200 more and sold it for Rs.300 more, his loss would have been only 20%. Find the initial CP.
Solution: Let initial CP = 5x (since 40% = 2/5). Initial SP = 3x.
New CP = 5x + 200. New SP = 3x + 300.
New Loss = 20% (1/5), so New SP = New CP × (4/5).
Equation: (5x + 200) × 4/5 = 3x + 300. Solving this gives x = 35.
Initial CP = 5 × 35 = Rs.175.

Module 3: Speed Hacks (Fractions & Unitary Method)

Toppers don't calculate, they multiply fractions.

The Fraction Hack:

16.66% = 1/6 (Profit) -> CP=6, SP=7
12.5% = 1/8 (Loss) -> CP=8, SP=7
28.56% ≈ 2/7 (Profit) -> CP=7, SP=9

The Unitary Method (Assume 100%):

Example: Sold an item for Rs.7,500 at a 25% profit. Find CP.
Solution: Assume CP = 100%. Profit = 25%, so SP = 125%.
125% = 7500. So 1% = 60. Therefore, 100% = Rs.6,000.

Module 4: The "Same Price" Conundrums (Crucial!)

This is where students lose easy marks. You must distinguish between "Same CP" and "Same SP".

Case A: Same CP (Cost Price)
If two items are bought at the same cost price, one sold at +x% and another at -x%, the net result is No Profit, No Loss.

Example: Bought two chairs for Rs.100 each. Sold one at +30% (Rs.130) and one at -30% (Rs.70). Total CP = Rs.200, Total SP = Rs.200. Net = 0%.

Case B: Same SP (Selling Price)
If two items are sold at the same selling price, one at +x% and another at -x%, it is Always a Loss.

Formula: Net Loss % = (x/10)²
Example: Sold two phones for Rs.120 each. One at +20% (CP = 100), one at -20% (CP = 150). Total CP = 250. Total SP = 240. Loss = 10/250 = 4%.
Balancing Method: +20% (5:6) and -20% (5:4). Make SP equal (LCM 12). Ratio becomes 10:12 and 15:12. Total CP = 25, Total SP = 24. Loss = 1/25 = 4%.

Module 5: The Art of Discounts

A discount is not a loss; it’s a reduction in the expected price (MP).

Successive Discounts:
Never add percentages directly. Use the multiplier method.

Formula: Final SP = MP × (1 - D1/100) × (1 - D2/100)
Example: MP = Rs.200. Discounts = 25% and 20%.
SP = 200 × 0.75 × 0.80 = Rs.120.
Shortcut for Overall Discount: -a - b + (ab/100) = -25 - 20 + 5 = -40%.

Tax + Discount (GST):
If an item is sold at a discount and tax is applied, the final price is calculated as:
Final Price = MP × (1 - Discount%) × (1 + Tax%)

Example: MP = Rs.10,000, Discount = 20%, GST = 10%.
SP = 10,000 × 0.8 × 1.1 = Rs.8,800.

Profit on SP vs. Profit on CP:

Example: A calculates profit on SP, B calculates on CP. SP is the same (Rs.520). A earns 25% profit (1/4 of SP), B earns 30% profit (3/10 of CP).
A: CP=3, SP=4. B: CP=10, SP=13.
Make SP equal (LCM 52). A = 39:52. B = 40:52.
Difference in profit = 1 unit = Rs.200. CP of A = 39 units = Rs.7,800

Module 6: Advanced Shenanigans (Freebies & Dishonest Dealers)

The "Buy X Get Y Free" Scheme:
Always calculate the Total CP of all items taken home, and Total SP of only the items paid for.

Example: Buy 4 get 1 free. CP per item = Rs.100. Total CP for 5 items = Rs.500. Discount = 10%. Profit = 20%. Find MP.
Equation: 4 × MP × 0.9 = 500 × 1.2.
3.6 × MP = 600 -> MP = Rs.166.67.

The Dishonest Dealer (Weight Cheating):
This is the ultimate test of logic. He cheats the wholesaler (buys more) and the customer (sells less).

Formula: Profit % = (Quantity Sold / Quantity Bought) - 1 (if selling at cost price).
Example: Buys 25% more (takes 125g for the price of 100g). Sells 20% less (gives 80g instead of 100g). He sells at cost price.
Profit % = (125 / 80) - 1 = 56.25%.
Combined with Markup & Discount: Markup 40%, Discount 15%, Cheats by 15% less weight.

CP = 100, MP = 140, SP = 140 × 0.85 = 119.
He gives 85g instead of 100g. CP of 85g = 85.
Profit % = (119 - 85) / 85 = 40%.

Module 7: Mains Level Mastery

At the Mains level, the questions become multi-layered.

Multi-Item Transactions with Ratios:

MP of TV : Refrigerator = 2 : 3. A regular customer gets 30% off on both. A new customer gets 20% off on TV and 25% off on Refrigerator. The shopkeeper earns 33.33% profit on TV and 25% profit on Refrigerator from the new customer. The difference in the amount paid by the new customer and the regular customer is Rs. 1750. Find the CP of 2 TVs and 1 Refrigerator.

Let MP of TV = 2x and Refrigerator = 3x.

Regular customer pays:
5x × 70% = 3.5x

New customer pays:
2x × 80% + 3x × 75% = 3.85x

Difference:
3.85x − 3.5x = 1750
x = 5000

TV SP = 1.6x = ₹8000
CP of TV = 8000 × 3/4 = ₹6000

Refrigerator SP = 2.25x = ₹11250
CP of Refrigerator = 11250 × 4/5 = ₹9000

Required CP:
2(6000) + 9000 = ₹21,000

2. Quadratic Equations + Profit & Loss:
Mains exams love to mix chapters.

Example: Roots of 4p² - (X+10)p - (162 + Y) = 0 are 14 and -4.5. Use X and Y to solve a profit/loss word problem.
Step 1: Sum of roots = 9.5 = (X+10)/4 -> X = 28.
Step 2: Product of roots = -63 = -(162+Y)/4 -> Y = 90.
Step 3: Use these values in the word problem (e.g., Ankur buying bottles at X-12 Rs each, etc.).

3. Data Sufficiency Strategy:
Don't solve fully! Just translate statements into equations.

Example: Rohan sold a cycle to Harish. Find Harish's SP if he sells it at 15% profit.
Statement I: Rohan marked up by 32% and offered Rs.340 discount. (We have SP but don't know CP).
Statement II: Sum of profits = Rs.645. (Can form an equation with one variable).
Statement III: Ratio of discount to MP is 17:72. (Can form an equation to find CP).
Conclusion: Statement I alone is insufficient. Statements II and III are individually sufficient.

💡 Final Takeaway

Profit, Loss, and Discount is not about memorizing 50 formulas. It's about understanding the Bridge (SP).