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Basic Profit & Loss

UP Police Constable · Quantitative Aptitude

Also prepare for:CRPF Const BSF Const CISF Const ITBP Const

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Core Concept

Read this first — the foundation of the topic

→Core Concept

When you buy something for Rs. 100 and sell it for Rs. 120, you make Rs. 20 profit. If you sell it for Rs. 80, you face Rs. 20 loss. This simple idea forms the basis of all profit-loss calculations

💡Key Terms

Cost Price (CP) = Price at which goods are purchased. Selling Price (SP) = Price at which goods are sold. Profit = SP - CP (when SP > CP). Loss = CP - SP (when CP > SP)

🔑Essential Formulas

Profit% = (Profit/CP) × 100. Loss% = (Loss/CP) × 100. SP = CP + Profit = CP(100 + Profit%)/100. SP = CP - Loss = CP(100 - Loss%)/100.

CP = SP × 100/(100 + Profit%). CP = SP × 100/(100 - Loss%).

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Exam Patterns

What examiners ask — read before attempting PYQs

✏️Example

20% profit on one item, 20% loss on another = Overall loss of 4%

✏️Worked Example 1

1

Identify CP = Rs. 800, SP = Rs. 920

2

Calculate Profit = SP - CP = 920 - 800 = Rs. 120

3

Apply formula Profit% = (Profit/CP) × 100 = (120/800) × 100 = 15% Answer: 15% profit Shortcut #2: Quick CP calculation when SP and profit% known. Use: CP = SP/(1 + Profit%/100). For 25% profit, divide SP by 1.25. For 20% loss, divide SP by 0.8

✏️Worked Example 2

1

SP = Rs. 1440, Loss% = 20%

2

Use shortcut CP = SP/(1 - Loss%/100) = SP/0.8

3

CP = 1440/0.8 = Rs. 1800 Verification: 20% of 1800 = 360, so SP = 1800 - 360 = 1440

→Answer

Rs. 1800 Shortcut #3: For successive transactions, multiply factors. 10% profit followed by 20% loss = 1.1 × 0.8 = 0.88, meaning 12% overall loss

→Most Common Trap

Students calculate percentage on Selling Price instead of Cost Price

💡Remember

Profit% and Loss% are ALWAYS calculated on Cost Price, never on Selling Price. This mistake costs at least 1-2 marks in every exam. Another frequent error involves sign confusion. When CP > SP, it's a loss situation. When SP > CP, it's profit.

Always check this relationship before applying formulas

📋Exam Strategy

Start with identifying what's given and what's asked. Write down CP, SP clearly. Apply the basic formula first, then use shortcuts for speed. Double-check by working backwards - if you found CP, calculate SP using the given profit% to verify your answer.

🔑 Key Points

Profit occurs when Selling Price > Cost Price, Loss occurs when Cost Price > Selling Price
Profit% and Loss% are always calculated on Cost Price, never on Selling Price
Quick formula: SP = CP × (100 ± gain%)/100 where + for profit, - for loss
Shortcut: When profit% equals loss% in two transactions, overall result is always loss
CP calculation trick: CP = SP/(1 + profit%/100) or CP = SP/(1 - loss%/100)
For successive discounts or profits, multiply the factors: (1±%/100)
Break-even point means SP = CP, so profit = 0 and loss = 0
Cost Price includes all expenses like transport, taxes, and overhead costs
Marked Price is different from Selling Price when discount is given
Overall loss% in equal profit-loss case = (profit%)²/100

📌 Exam Facts

When profit% = loss% = x%, then overall loss% = x²/100
If an article is sold at cost price after giving x% discount, then markup% = x/(100-x) × 100
For 2 articles with equal CP, one sold at x% profit and other at x% loss, overall loss = 2x²/(100)²
When SP of x articles = CP of y articles, profit% = (y-x)/x × 100
If CP of A is x% more than CP of B, then CP of B is x/(100+x) × 100% less than A
Selling price formula: SP = MP × (100-discount%)/100 where MP is Marked Price
For successive profits of a% and b%, overall profit% = a + b + ab/100
Break-even occurs when SP = CP, meaning profit percentage = 0%

🚀 60-Second Revision

Remember: Profit% = (SP-CP)/CP × 100, always on cost price base
Formula: CP = SP/(1 ± gain%/100) for quick reverse calculations
Trap: Never calculate profit percentage on selling price
Shortcut: Equal profit-loss case always gives overall loss = (%)²/100
Quick check: SP > CP means profit, CP > SP means loss
Pattern: Successive changes multiply as (1±%/100) factors
Memory aid: Cost price is the denominator in all percentage calculations

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