Percentages, Profit & Loss for SSC CGL - Formulas, Tricks & Examples

What are Percentages, Profit & Loss? These are fundamental business mathematics concepts that test your ability to calculate profits, losses, discounts, and percentage changes. For SSC CGL, these topics appear in both Tier I and Tier II with practical, real-world applications.

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1. Basic Percentage Concepts

What is Percentage? Percentage means "per hundred" - it's a way to express a number as a fraction of 100. The symbol % means "out of 100".

Essential Percentage Formulas

Understanding Percentage

If you have 30 out of 100, you have 30%. This basic concept extends to profit percentages (profit on cost price), loss percentages, discount percentages, and more.

Percentage Formula

Percentage = (Part/Whole) × 100

Example: What percentage is 15 of 60?

Percentage = (15/60) × 100 = 25%

Percentage Increase

% Increase = [(New - Original)/Original] × 100

Example: Price increased from ₹80 to ₹100

% Increase = [(100-80)/80] × 100 = 25%

Percentage Decrease

% Decrease = [(Original - New)/Original] × 100

Example: Price decreased from ₹120 to ₹90

% Decrease = [(120-90)/120] × 100 = 25%

SSC Shortcut: Quick Percentage Calculations

10%: Move decimal one place left (₹250 → 10% = ₹25)

5%: Half of 10% (₹250 → 5% = ₹12.50)

20%: Double of 10% (₹250 → 20% = ₹50)

25%: One-fourth or half of half (₹250 → 25% = ₹62.50)

Solved Example: Percentage Application

Q: If a number is increased by 20% and then decreased by 20%, what is the net percentage change?

Let original number = 100

Step 1: Increase by 20%
100 + 20% of 100 = 100 + 20 = 120

Step 2: Decrease by 20%
120 - 20% of 120 = 120 - 24 = 96

Step 3: Net change
Original = 100, Final = 96
Decrease = 4
% Decrease = (4/100) × 100 = 4% decrease

Key Insight: Same percentages of increase and decrease don't cancel out!

2. Profit & Loss Fundamentals

What is Profit & Loss? Profit occurs when Selling Price (SP) > Cost Price (CP). Loss occurs when SP < CP.

Key Terms & Formulas

Term Abbreviation Meaning Formula Cost Price CP Price at which item is bought Base price Selling Price SP Price at which item is sold CP ± Profit/Loss Profit P SP > CP SP - CP Loss L SP < CP CP - SP Profit % P% Profit as % of CP (Profit/CP) × 100 Loss % L% Loss as % of CP (Loss/CP) × 100

Important Formulas

Profit = SP - CP
Loss = CP - SP
Profit % = (Profit/CP) × 100
Loss % = (Loss/CP) × 100
SP = CP × (100 + P%)/100 (for profit)
SP = CP × (100 - L%)/100 (for loss)

Common Mistakes

Calculating % on SP instead of CP
Mixing up profit% and loss% formulas
Forgetting to convert % to decimal
Using wrong base for percentage calculation

SSC Shortcut: Direct Formula Application

When CP and Profit% given: SP = CP × (100 + P%)/100

When CP and Loss% given: SP = CP × (100 - L%)/100

When SP and Profit% given: CP = SP × 100/(100 + P%)

When SP and Loss% given: CP = SP × 100/(100 - L%)

Solved Example: SSC Pattern Question

Q: A shopkeeper sells an article at 20% profit. If he had bought it at 10% less and sold it for ₹18 less, he would have gained 25%. Find the cost price of the article.

Step 1: Let original CP = ₹100 (assume for easy calculation)
Original SP = 100 + 20% of 100 = ₹120

Step 2: New CP = 10% less = 100 - 10 = ₹90
New SP = ₹18 less than original SP = 120 - 18 = ₹102

Step 3: Profit on new transaction = 102 - 90 = ₹12
Profit % = (12/90) × 100 = 13.33%
But question says he would have gained 25%

Step 4: Our assumption CP=100 gives wrong profit%. So scale proportionally:
When CP=100, difference in profit% = 25% - 13.33% = 11.67%
Actual difference should be 25% - 20% = 5%
Scale factor = 5/11.67 ≈ 0.4286

Step 5: Actual CP = 100/0.4286 ≈ ₹233.33

Alternative Quick Method:
Let CP = x
SP = 1.2x
New CP = 0.9x
New SP = 1.2x - 18
Given: (1.2x - 18 - 0.9x)/0.9x = 0.25
Solve: (0.3x - 18)/0.9x = 0.25
0.3x - 18 = 0.225x
0.075x = 18
x = 240

Final Answer: CP = ₹240

3. Discount Problems & Marked Price

What is Discount? Reduction given on the Marked Price (MP) or List Price to attract customers.

Discount Formulas & Concepts

Understanding Discount Structure

Marked Price (MP) is the price displayed on the item. Selling Price (SP) is what customer actually pays after discount. Discount is always calculated on Marked Price.

Basic Discount Formulas

Discount = MP - SP
Discount % = (Discount/MP) × 100
SP = MP × (100 - D%)/100
MP = SP × 100/(100 - D%)

Example: MP = ₹500, Discount = 20%, Find SP

SP = 500 × (100-20)/100 = 500 × 0.8 = ₹400

Successive Discounts

When multiple discounts are given one after another:

Effective discount = 100 - [(100-d₁)(100-d₂).../100^(n-1)]

Example: 20% and 10% successive discounts

Effective = 100 - [(100-20)(100-10)/100]
= 100 - [80×90/100] = 100 - 72 = 28%

Profit after Discount

When shopkeeper gives discount but still makes profit:

CP = MP × (100 - D%)/(100 + P%)

MP=₹1000, D=20%, P=25%, Find CP

CP = 1000 × (100-20)/(100+25)
= 1000 × 80/125 = ₹640

SSC Shortcut: Quick Discount Calculations

Two discounts a% and b%: Net discount = a + b - (ab/100)

Three discounts a%, b%, c%: Net = a + b + c - (ab+bc+ca)/100 + (abc)/10000

Special case: Two discounts of 20% and 25% → Not 45%!
Actual = 20 + 25 - (20×25/100) = 45 - 5 = 40%

Solved Example: Complex Discount Problem

Q: A shopkeeper marks his goods 30% above CP and gives 10% discount to customer. If he also uses a faulty weight that gives 20% less quantity, what is his net profit percentage?

Step 1: Assume CP for 1000g = ₹100
(So CP per gram = ₹0.10)

Step 2: MP = 30% above CP = ₹130 for 1000g

Step 3: Discount 10% on MP
SP = 130 × 0.9 = ₹117 for 1000g

Step 4: But gives only 800g (20% less)
CP for 800g = 800 × 0.10 = ₹80
SP for 800g = ₹117 (charges for 1000g but gives 800g)

Step 5: Actual profit = 117 - 80 = ₹37
Profit % = (37/80) × 100 = 46.25%

Key Insight: Dishonest practices significantly increase profit!

4. Successive Percentage Changes

What are Successive Percentages? When multiple percentage changes (increase/decrease) are applied one after another.

Methods & Formulas

Understanding the Concept

If a number increases by 10% and then decreases by 10%, the net effect is NOT 0%! Each percentage change is applied on the new value, not the original.

Two Successive Changes

Net % change = a + b + (ab/100)

Note: Use + for increase, - for decrease

Increase 20% then decrease 15%

Net = 20 - 15 + (20×-15/100)
= 5 - 3 = 2% increase

Three Successive Changes

Net = a + b + c + (ab+bc+ca)/100 + (abc)/10000

10%, 20%, 30% increases

Net = 10+20+30 + (200+600+300)/100 + (6000)/10000
= 60 + 11 + 0.6 = 71.6% increase

Equal Successive Changes

When same % change happens 'n' times:

Final = Original × (1 ± r/100)^n

Increase 10% every year for 3 years

Final = Original × (1.10)³
= Original × 1.331
Net increase = 33.1%

SSC Shortcut: Quick Successive Calculations

Two equal increases of x%: Net > 2x%

Two equal decreases of x%: Net < 2x% (more decrease)

Increase x% then decrease x%: Net decrease of (x²/100)%

Example: 20% increase then 20% decrease → Net = 4% decrease

Solved Example: Population Growth

Q: The population of a town increases by 10% in the first year, decreases by 15% in the second year, and increases by 20% in the third year. If the final population is 56,232, find the original population.

Method 1: Using net percentage formula
Net effect = 10 - 15 + 20 + [10×(-15) + (-15)×20 + 20×10]/100 + [10×(-15)×20]/10000
= 15 + [-150 -300 + 200]/100 + [-3000]/10000
= 15 + (-250/100) - 0.3
= 15 - 2.5 - 0.3 = 12.2% increase

Method 2: Using multiplication factor (easier)
Let original population = P
After 1st year: P × 1.10 = 1.1P
After 2nd year: 1.1P × 0.85 = 0.935P
After 3rd year: 0.935P × 1.20 = 1.122P

1.122P = 56,232
P = 56,232 ÷ 1.122 = 50,100

Final Answer: Original population = 50,100

5. CP, MP, SP Relationships

Understanding the Price Chain: Cost Price → Marked Price → Selling Price → Profit/Loss

Complete Price Relationships

Situation Given To Find Formula Profit after Discount MP, D%, P% CP CP = MP × (100-D%)/(100+P%) Discount to Break Even CP, MP Max D% for no loss D% = [(MP-CP)/MP] × 100 Required Markup CP, D%, Desired P% MP MP = CP × (100+P%)/(100-D%) Double Discount MP, D1%, D2% SP SP = MP × (100-D1)/100 × (100-D2)/100 Profit/Loss Conversion If P% becomes L% SP Difference Difference = CP × |P% + L%|/100

SSC Shortcut: Quick Relationships

When MP is x% above CP and D% discount given:
Actual P% = x - D - (xD/100)

To make P% profit after D% discount:
Markup % = (P + D) × 100/(100 - D)

Example: Want 20% profit after 10% discount:
Markup = (20+10)×100/90 = 3000/90 = 33.33%

Solved Example: Complex Price Chain

Q: A shopkeeper marks an article at such a price that after giving 15% discount, he makes 20% profit. If the cost price increases by 12% and he still wants to make 20% profit after 15% discount, by how much should he increase the marked price?

Step 1: Let original CP = ₹100
Desired profit 20% → SP = ₹120
This SP is after 15% discount on MP

Step 2: SP = MP × (100-15)/100
120 = MP × 0.85
MP = 120/0.85 = ₹141.18 (approx)

Step 3: New CP = 100 + 12% = ₹112
Desired profit still 20% → New SP = 112 × 1.20 = ₹134.40

Step 4: New SP = New MP × 0.85
134.40 = New MP × 0.85
New MP = 134.40/0.85 = ₹158.12 (approx)

Step 5: Increase in MP = 158.12 - 141.18 = ₹16.94
Percentage increase = (16.94/141.18) × 100 ≈ 12%

Quick Method:
When CP increases by x%, to maintain same profit% after same discount%, MP should increase by same x%!
So directly: MP increase = 12%

Final Answer: 12% increase in marked price

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Frequently Asked Questions

Q1: How many questions from Percentages & Profit-Loss in SSC CGL?

Answer: Typically 6-8 questions in Tier I and 10-15 questions in Tier II. This is one of the highest weightage topics in Quantitative Aptitude section.

Q2: What's the difference between profit% calculated on CP vs SP?

Answer: Profit% is always calculated on Cost Price unless specified otherwise. Some problems may say "profit on selling price" - then base changes to SP. Always read carefully!

Q3: How to solve successive discount problems quickly?

Answer: Use the formula: Net discount = a + b - (ab/100) for two discounts. For three: a + b + c - (ab+bc+ca)/100 + (abc)/10000. Better method: Use multiplication factors (0.8 for 20% discount, etc.)

Q4: What if profit and loss percentages are same but SP differs?

Answer: If an article is sold at two different SP with same profit% and loss%, then CP = (SP1 + SP2)/2. This is a common SSC shortcut.

Q5: How to handle "faulty weight" problems?

Answer: Convert everything to per unit weight. If seller uses 900g instead of 1000g, he's actually selling 900g at price of 1000g. Calculate CP for quantity given, SP for quantity charged.

Q6: What's the quickest way to verify profit-loss answers?

Answer: Assume CP = ₹100 for easy calculation. Work through the problem with this assumption, then scale to actual values. This avoids fractions and decimals in intermediate steps.

Final Exam Strategy for Percentages & Profit-Loss

Time Allocation: Basic problems: 20-30 seconds, Complex problems: 60-90 seconds.

Priority Order: 1) Direct formula application, 2) Discount problems, 3) Successive percentages, 4) Complex profit-loss chains.

Accuracy Check: Verify with CP=100 assumption. If answer seems unreasonable, re-check percentage base.

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