Profit, Loss & Discount
SSC-CGL Exams
1. Introduction
Profit, Loss, and Discount questions check your understanding of cost, selling, and marked price relations. They are among the most scoring topics in SSC exams — once you master the formulas and common traps like successive discounts or false weights. Let's learn all concepts step-by-step.
2. Basic Concepts & Formulas
| Term | Meaning |
|---|---|
| Cost Price (C.P.) | The price at which an article is bought |
| Selling Price (S.P.) | The price at which it is sold |
| Marked Price (M.P.) | The printed price before discount |
| Discount (D) | The reduction given on the marked price |
Profit / Gain
When S.P. > C.P.
Profit = S.P. - C.P.
Profit% = (Profit / C.P.) × 100
Loss
When C.P. > S.P.
Loss = C.P. - S.P.
Loss% = (Loss / C.P.) × 100
Relation Between C.P. and S.P.
S.P. = C.P. × (1 + Gain%/100)
C.P. = S.P. × (1 - Gain%/100)
S.P. = C.P. × (1 - Loss%/100)
Trick to Remember: Always take C.P. as the base for % profit or % loss.
3. Marked Price and Discount
| Formula | Meaning |
|---|---|
| Discount = M.P. - S.P. | Direct difference |
| Discount% = (Discount / M.P.) × 100 | Based on M.P. |
| S.P. = M.P. × (1 - Discount% / 100) | Final price after discount |
Example 1
A shopkeeper marks an item at ₹1000 and allows a discount of 20%. Find the selling price.
S.P. = 1000 × (1 - 20/100) = ₹800
Example 2 (Profit after Discount)
An article is marked at ₹600, discount 10%, and cost price ₹450. Find the profit%.
S.P. = 600 × (1 - 0.10) = ₹540
Profit = 540 - 450 = 90
Profit% = (90/450) × 100 = 20%
Answer: Profit = 20%
4. Successive Discounts (Discount Chain)
When two discounts are given — say 20% and 10%,
Net Discount% = A + B - (AB/100)
Example
M.P. = ₹2000, two successive discounts of 20% and 10%
Net Discount% = 20 + 10 - (20×10)/100 = 28%
S.P. = 2000 × (1 - 28/100) = ₹1440
Answer: Selling Price = ₹1440
5. False Weights (Cheating by Weight)
Sometimes shopkeepers sell goods at a profit even at cost price by using less weight.
Gain% = [100 × Error] / (True Weight - Error)
Example
A shopkeeper sells goods at cost price but uses 900g instead of 1kg.
Gain% = [100 × 100] / (1000 - 100) = 10000/900 = 11.11%
Answer: 11.11% profit
6. Practice with SSC-style Examples
Q1. A man buys a watch for ₹800 and sells it for ₹960. Find his profit%.
View Answer
Profit = 960 - 800 = ₹160
Profit% = (160/800) × 100 = 20%
Q2. A trader sells goods at 10% loss. If he had sold it for ₹540 more, he would have gained 8%. Find the cost price.
View Answer
Difference in % = 8 + 10 = 18%
So, 18% of C.P. = ₹540
⇒ C.P. = (540 × 100) / 18 = ₹3000
Q3. A shopkeeper offers two successive discounts of 20% and 10%. Find the net discount.
View Answer
Net Discount = 20 + 10 - (20×10)/100 = 28%
Q4. Find the selling price if M.P. = ₹1500 and discount = 25%.
View Answer
S.P. = 1500 × (1 - 0.25) = ₹1125
Q5. A dishonest dealer professes to sell goods at cost price but uses 850g instead of 1kg. Find his gain%.
View Answer
Gain% = (100 × 150) / (1000 - 150) = 15000/850 = 17.65%
Q6. A man sells two articles for ₹1200 each. On one he gains 20%, on the other he loses 20%. Find his overall gain or loss%.
View Answer
C.P.₁ = 100, S.P.₁ = 120
C.P.₂ = 100, S.P.₂ = 80
Total C.P. = 100 + 125 = 225
Total S.P. = 120 + 80 = 200
Loss% = (25/225) × 100 = 11.11% loss
Q7. A merchant marks his goods 40% above cost price and allows a discount of 25%. Find profit%.
View Answer
C.P. = ₹100 → M.P. = ₹140
Discount = 25% of 140 = ₹35 → S.P. = ₹105
Profit% = 5%
Answer: 5% Profit
7. Quick Summary Table
| Concept | Formula |
|---|---|
| Profit% | (Profit / C.P.) × 100 |
| Loss% | (Loss / C.P.) × 100 |
| S.P. | C.P. × (1 ± Gain/Loss%) |
| Discount% | (Discount / M.P.) × 100 |
| Successive Discounts | A + B - (AB/100) |
| False Weight Gain% | (100 × Error) / (True Weight - Error) |
You've completed Article 3: Profit, Loss & Discount!
Courage Tip: Always visualize the flow of price — C.P. → M.P. → Discount → S.P. Once you control that chain, this topic becomes your fastest-scoring weapon in SSC CGL.
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