Profit and Loss – Formula, Tricks, and Examples
Profit and Loss – Formula, Tricks, and Examples
Profit and Loss is one of the most important topics in Quantitative Aptitude. Questions from this chapter are frequently asked in competitive exams such as SSC, Banking, Railway, CAT, and placement tests.
If students understand the basic concepts, formulas, and shortcuts of Profit and Loss properly, they can solve questions faster and with better accuracy.
Quick Summary
Profit
When SP > CP, there is a profit.
Loss
When SP < CP, there is a loss.
Important Use
Very common in aptitude exams and daily calculation problems.
What is Profit and Loss?
Profit
When the Selling Price (SP) of an item is greater than the Cost Price (CP), the seller makes a profit.
Profit = SP - CP
Loss
When the Selling Price (SP) of an item is less than the Cost Price (CP), the seller incurs a loss.
Loss = CP - SP
Important Terms in Profit and Loss
| Term | Meaning |
|---|---|
| Cost Price (CP) | Price at which an item is purchased. |
| Selling Price (SP) | Price at which an item is sold. |
| Profit | Gain when SP is greater than CP. |
| Loss | Loss when SP is less than CP. |
| Marked Price (MP) | Price written on the product. |
| Discount | Reduction in the marked price. |
Profit and Loss Formulas
1. Profit Formula
Profit = Selling Price - Cost Price
Example: CP = ₹500, SP = ₹600, Profit = ₹100
2. Loss Formula
Loss = Cost Price - Selling Price
Example: CP = ₹700, SP = ₹650, Loss = ₹50
3. Profit Percentage
Profit % = (Profit / Cost Price) × 100
Example: CP = ₹400, SP = ₹500, Profit % = 25%
4. Loss Percentage
Loss % = (Loss / Cost Price) × 100
Example: CP = ₹500, SP = ₹450, Loss % = 10%
5. Selling Price Formula
SP = CP × (100 + Profit%) / 100
Example: CP = ₹200, Profit = 20%, SP = ₹240
6. Selling Price with Loss
SP = CP × (100 - Loss%) / 100
Example: CP = ₹500, Loss = 10%, SP = ₹450
7. Cost Price Formula
CP = SP × 100 / (100 + Profit%)
Example: SP = ₹360, Profit = 20%, CP = ₹300
8. Cost Price with Loss
CP = SP × 100 / (100 - Loss%)
Example: SP = ₹450, Loss = 10%, CP = ₹500
9. Discount Formula
Discount = Marked Price - Selling PriceDiscount % = (Discount / Marked Price) × 100
Example: MP = ₹1000, SP = ₹800, Discount % = 20%
10. Marked Price Formula
MP = SP × 100 / (100 - Discount%)
Example: SP = ₹800, Discount = 20%, MP = ₹1000
Important Tricks for Profit and Loss
Trick 1
If a shopkeeper gains 20%, then
SP = 1.2 × CP
Trick 2
If a shopkeeper loses 20%, then
SP = 0.8 × CP
Trick 3: Successive Discounts
Total Discount Formula:
Total Discount = a + b - (ab / 100)
Example: Discounts = 20% and 10%
Total Discount = 20 + 10 - (20 × 10 / 100) = 28%
Example Questions
Question 1
A shopkeeper buys a book for ₹200 and sells it for ₹250. Find the profit percentage.
Profit = 250 - 200 = 50
Profit % = (50 / 200) × 100 = 25%
Question 2
A trader sells an item at ₹450 with a loss of 10%. Find the cost price.
CP = SP × 100 / (100 - Loss%)
CP = 450 × 100 / 90 = ₹500
Question 3
The marked price of a shirt is ₹1200. A discount of 25% is given. Find the selling price.
SP = MP × (100 - Discount) / 100
SP = 1200 × 75 / 100 = ₹900
हिंदी में – लाभ और हानि
अब इसी टॉपिक को आसान हिंदी में समझते हैं।
लाभ और हानि गणित के Quantitative Aptitude का एक महत्वपूर्ण अध्याय है। इस टॉपिक से SSC, Banking, Railway, CAT और placement tests में अक्सर प्रश्न पूछे जाते हैं।
यदि छात्र Profit and Loss के basic concepts और formulas को अच्छे से समझ लें, तो वे प्रश्नों को जल्दी और सही तरीके से हल कर सकते हैं।
लाभ (Profit)
जब किसी वस्तु का विक्रय मूल्य (SP), क्रय मूल्य (CP) से अधिक होता है, तो लाभ होता है।
लाभ = SP - CP
हानि (Loss)
जब किसी वस्तु का विक्रय मूल्य (SP), क्रय मूल्य (CP) से कम होता है, तो हानि होती है।
हानि = CP - SP
महत्वपूर्ण शब्द
- क्रय मूल्य (CP): जिस मूल्य पर वस्तु खरीदी जाती है।
- विक्रय मूल्य (SP): जिस मूल्य पर वस्तु बेची जाती है।
- लाभ: जब SP, CP से अधिक हो।
- हानि: जब SP, CP से कम हो।
- अंकित मूल्य (MP): वस्तु पर लिखा हुआ मूल्य।
- छूट (Discount): अंकित मूल्य में दी गई कमी।
महत्वपूर्ण सूत्र
लाभ = SP - CPहानि = CP - SPलाभ % = (लाभ / CP) × 100हानि % = (हानि / CP) × 100SP = CP × (100 + लाभ%) / 100SP = CP × (100 - हानि%) / 100CP = SP × 100 / (100 + लाभ%)CP = SP × 100 / (100 - हानि%)छूट = MP - SPछूट % = (छूट / MP) × 100MP = SP × 100 / (100 - छूट%)उदाहरण
उदाहरण 1
CP = ₹500
SP = ₹600
लाभ = ₹100
उदाहरण 2
CP = ₹700
SP = ₹650
हानि = ₹50
उदाहरण 3
CP = ₹400
SP = ₹500
लाभ % = 25%
उदाहरण 4
MP = ₹1200
छूट = 25%
SP = ₹900
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