Cost Price and Selling Price — Revision Notes

⚡ 30-Second Revision

CP: — Cost Price (Purchase + Overheads)
SP: — Selling Price (Final price to customer)
Profit: — SP > CP (P = SP - CP)
Loss: — CP > SP (L = CP - SP)
%P: — (Profit/CP)*100
%L: — (Loss/CP)*100
MP: — Marked Price (List Price)
Discount: — Reduction on MP (D = MP - SP)
%D: — (Discount/MP)*100
Key Formula: — SP = CP * (100 ± %P or %L)/100
Key Formula: — SP = MP * (100 - %D)/100
Successive Discounts: — Not additive, apply sequentially.
Dishonest Dealer: — Profit on (True Weight - False Weight) / False Weight.

2-Minute Revision

For a quick yet comprehensive review of Cost Price and Selling Price, focus on the core definitions and their interrelationships. Remember that Cost Price (CP) is your total expenditure, including purchase price and any overheads.

Selling Price (SP) is your revenue. The difference determines Profit (SP > CP) or Loss (CP > SP). Crucially, Profit and Loss Percentages are always calculated on CP unless stated otherwise.

So, if you have a 20% profit, SP is 120% of CP. If a 10% loss, SP is 90% of CP.

Next, grasp Marked Price (MP) and Discount. MP is the listed price, and Discounts are always calculated on MP. The SP after discount is MP minus the discount amount. Be wary of successive discounts; they are applied sequentially, not additively.

For complex problems, consider the ratio method (e.g., 20% profit means CP:SP = 5:6) or the successive percentage change formula. Always identify the correct base for each percentage calculation to avoid common traps.

Practice problems involving overheads and dishonest dealers, as these are frequent in CSAT. This rapid recall ensures you have the fundamental tools ready for any problem.

5-Minute Revision

A thorough five-minute revision for Cost Price and Selling Price demands a structured approach, ensuring all critical aspects are covered. Start by solidifying the foundational definitions: Cost Price (CP) as the total expenditure (purchase + overheads), Selling Price (SP) as the revenue, and Marked Price (MP) as the listed price.

Clearly distinguish between Profit (SP > CP) and Loss (CP > SP), and their respective percentage calculations, always recalling that the base for these is CP. For instance, a 25% profit means SP = 1.

25 * CP, and a 20% loss means SP = 0.80 * CP. This understanding allows you to move fluidly between CP and SP.

Next, focus on the role of Discount. Discounts are reductions on the MP, leading to the SP. Remember the formula SP = MP * (100 - Discount%)/100. A critical point is that discounts are *never* calculated on CP.

Pay special attention to successive discounts, where each discount is applied to the *reduced* price, not the original MP. The net percentage change formula (A + B + AB/100) can be a powerful shortcut here.

Review dishonest dealer problems, where the profit is calculated on the actual quantity sold, not the quantity professed. For example, selling 800g for 1kg's price yields profit on 800g. Finally, mentally walk through the common pitfalls: confusing profit on CP vs.

SP, adding successive discounts, and ignoring overheads. Ensure you can quickly set up equations for multi-step problems and apply the most efficient method (unitary, algebraic, or ratio) based on the problem's structure.

This comprehensive mental walkthrough prepares you for diverse CSAT questions.

Prelims Revision Notes

For UPSC CSAT Prelims, recall these key facts and formulas for Cost Price and Selling Price:

CP (Cost Price): — Purchase Price + Overheads (transport, labor, etc.). This is your base.
SP (Selling Price): — The price at which an item is sold.
Profit: — SP - CP (when SP > CP).
Loss: — CP - SP (when CP > SP).
Profit %: — (Profit / CP) * 100. Always on CP.
Loss %: — (Loss / CP) * 100. Always on CP.
MP (Marked Price): — List Price / Tag Price. Price before discount.
Discount: — MP - SP. Reduction on MP.
Discount %: — (Discount / MP) * 100. Always on MP.

Key Formula Relationships:

SP = CP * (100 + Profit%) / 100
SP = CP * (100 - Loss%) / 100
CP = SP * 100 / (100 + Profit%)
CP = SP * 100 / (100 - Loss%)
SP = MP * (100 - Discount%) / 100

UPSC CSAT Specifics & Shortcuts:

Successive Discounts: — Apply sequentially. Net Discount % = A + B - (AB/100). (e.g., 20%, 10% -> 20+10-(20*10)/100 = 28% net discount).
Equal SP, Equal %P/%L: — If two items sold at same SP, one X% profit, other X% loss, overall loss is (X/10)^2 %.
Dishonest Dealer (False Weight): — If uses 'x' for 'y' (y>x), Profit % = ((y-x)/x) * 100.
Profit Margin vs. Profit Percentage: — Profit Margin is on SP, Profit Percentage is on CP. Be careful with the base.
Ratio Method: — Convert percentages to fractions (e.g., 20% profit = 1/5 profit on CP. If CP=5 units, Profit=1 unit, SP=6 units). This is very efficient.

Common Traps to Avoid:

Calculating profit/loss on SP (unless stated).
Calculating discount on CP.
Adding successive discounts directly.
Ignoring overheads in CP.
Not equalizing quantities in 'articles for rupees' problems.

Mains Revision Notes

For a Mains-oriented revision of Cost Price and Selling Price, the focus shifts from mere calculation to conceptual depth and analytical application, particularly relevant for General Studies Paper III (Economy) and logical reasoning in CSAT. The core framework involves understanding the strategic interplay of CP, SP, MP, and Discount.

1. Conceptual Hierarchy & Interdependence:

* CP (Cost Price): The absolute baseline. Represents resource allocation and production cost. Consider how factors like input costs, labor, and technology influence CP. This connects to supply-side economics.

* MP (Marked Price): A strategic pricing tool. It's the 'anchor' for discounts, allowing flexibility in sales and marketing. Reflects market positioning and competitive strategy. * SP (Selling Price): The realized revenue.

Directly impacts profitability. Influenced by market demand, competition, and pricing strategies (e.g., penetration pricing, skimming). * Discount: A tactical tool to stimulate demand, clear inventory, or respond to competition.

Analyze its impact on SP and overall profit margins.

2. Profitability Analysis:

* Profit % (on CP): The true measure of return on investment. Essential for internal business analysis and comparing efficiency. * Profit Margin (on SP): Often used in sales and marketing. Understand its distinction from profit percentage and why it can be misleading if not contextualized. * Break-even Analysis: The point where SP = CP. Crucial for understanding minimum sales targets and viability. Relate this to fixed and variable costs in economics.

3. Real-World Applications & Policy Linkages:

* Government Intervention: How MSPs (Minimum Support Prices) act as a floor for CP for farmers, influencing their profitability and market SP. Price controls (e.g., essential commodities) directly impact SP.

* Consumer Protection: 'Dishonest dealer' problems highlight issues of market ethics, consumer fraud, and the role of regulatory bodies (e.g., Bureau of Indian Standards, Weights and Measures Department).

* Market Dynamics: Analyze how competition drives discount strategies (MP to SP) and impacts overall profit margins across industries.

4. Analytical Framework for Problem Solving:

* Deconstruct: Break down complex problems into sequential steps (CP -> MP -> SP). Identify the base for each percentage calculation. * Critical Thinking: For CSAT, go beyond calculation. Ask: 'What is the problem testing?' (e.g., conceptual clarity, attention to detail, multi-step reasoning). * Efficiency: Choose the most appropriate method (algebraic for complex, ratio for percentages, shortcuts for specific patterns) to optimize time.

This holistic approach ensures that CP and SP are viewed not just as math problems but as fundamental building blocks for economic reasoning and policy analysis.

Vyyuha Quick Recall

VYYUHA QUICK RECALL: CPSP-MAGIC

C - Cost Price: Complete Cost (Purchase + Overheads) P - Profit/Loss: Percentage on Purchase (CP is the base) S - Selling Price: Sales Sum (Final amount received) P - Percentages: Precise Percentage (Convert to fractions for speed)

M - Marked Price: Maximum Money (Listed price, before discount) A - Always Discount on MP: Always Apply to MP G - Get the Sequence Right: Go CP -> MP -> SP I - Ignore Additive Discounts: Instead, apply sequentially C - Check for Dishonesty: Calculate on actual quantity sold

Visual Memory Aids:

1
The 'CP-SP-MP Mountain': — Imagine a mountain. CP is at the base (foundation). MP is the peak (highest price). SP is somewhere on the slope (after discount). Profit is climbing from CP to SP. Loss is sliding down from CP to SP. Discount is falling from MP to SP.
2
The 'Percentage Wheel': — Visualize a wheel with CP at its center. Profit/Loss percentages 'spin' out from CP. A smaller wheel for MP, with Discount percentages 'spinning' out from MP. This reinforces that they have different bases.