Profit, Loss & Discount

Profit, Loss & Discount

🟢 Lite

Key Rule / Formula

Profit% = (SP − CP)/CP × 100. Loss% = (CP − SP)/CP × 100. Discount% = (MP − SP)/MP × 100. Always identify which two of CP, SP, MP are involved before calculating.

Memory Trick

SP = CP × (1 + Profit%)/100 for a gain. SP = CP × (100 − Loss)/100 for a loss. For discount: SP = MP × (100 − Discount%)/100. If no discount is mentioned, MP = CP (marked at cost price), which means no discount applies.

1-Sentence Summary

SSC tests the full chain of relationships between Cost Price (what you pay), Selling Price (what you receive), and Marked Price (the listed price before discount) — identify the two relevant values first, then apply the appropriate formula.

Quick Example

Q: An article is sold for ₹360 at a loss of 10%. Find the cost price. A: SP = CP × (100 − Loss)/100 → 360 = CP × 0.90 → CP = 360 ÷ 0.90 = ₹400

Q: A shopkeeper offers a 15% discount on an article with MP of ₹800 and still makes a 20% profit. Find the CP. A: SP after discount = 800 × 0.85 = ₹680. Since profit = 20%: SP = CP × 1.20 → CP = 680 ÷ 1.20 = ₹566.67

Must Remember

• Successive discounts: If an article has two discounts (say 20% and 10%), the final SP = MP × 0.80 × 0.90 — NOT MP minus 30%.
• Finding CP when SP and gain% given: CP = SP ÷ (1 + Gain%/100).
• False weights/fake goods: If a shopkeeper uses 900g as 1kg (false scale), his effective gain = (1000 − 900)/900 × 100 = 11.11%.
• Equivalent discount for successive discounts: For two discounts d₁ and d₂ on MP, equivalent single discount = (1 − (1−d₁)(1−d₂)) × 100.

Exam Tips for SSC CGL Tier 2

• Always find CP first when MP is given — it helps anchor all other calculations.
• When profit percentage and loss percentage are equal on two different transactions at the same CP, there is no net profit or loss.
• A shopkeeper giving a discount of X% but also using false weights (short weight) means his actual gain% is higher than it appears.
• Break-even: when SP = CP, profit% = 0, loss% = 0.

Common Pitfalls

• Confusing MP with CP: MP is just the tag price. If a shopkeeper buys at CP and marks up to MP, the profit calculation uses CP, not MP.
• Treating successive discounts as subtractive: 20% + 10% off does NOT equal 30% off. Two 10% discounts = 0.90 × 0.90 = 0.81 = 19% total discount, not 20%.
• Using SP as the base for profit/loss calculation: Never. Profit/Loss is always relative to CP.
• Forgetting to convert percentage to decimal before multiplying: 20% gain = ×1.20, not ×1.20 with the 20 left as 20.

🟡 Standard

Concept

Profit and loss are fundamentally percentage calculations on the cost price. The selling price (SP) is what the buyer pays, cost price (CP) is what the seller spends. When SP > CP, profit = SP − CP; when SP < CP, loss = CP − SP. The complication in SSC questions is that overhead costs (transport, packaging, octroi) must be added to CP before calculating profit/loss, and discounts are always applied on the marked price (MP), not the cost price.

Discount questions involve three prices: MP (what the seller initially tags), SP (what the buyer actually pays), and CP (what the seller paid). A common Tier 2 question is: “A shopkeeper gives a discount of 20% and still makes a 10% profit. Find the markup percentage” — meaning by how much above cost did he mark the price initially?

Fake transactions and weighing errors are a recurring theme: if a shopkeeper uses false weights (sells 900g when claiming 1kg), his effective profit is calculated on the difference.

Key Points

• Gain% = (Gain/CP) × 100. Loss% = (Loss/CP) × 100. Always take CP as base for percentages.
• When a transaction involves profit of x% and loss of y% on false weights, effective profit = x + y + xy/100.
• Discount is always on MP. Profit/Loss is always on CP.
• If SP with two different profit percentages is equal, CP can be found using the weighted average formula.
• Markup = (MP − CP)/CP × 100. After discount d%, SP = MP × (1 − d/100).

Worked Example

Q: A shopkeeper buys an article at 20% below its marked price. He sells it at a 10% discount on the marked price. Find his profit percent. Approach: Let MP = ₹100. CP = 100 − 20% of 100 = ₹80. SP = 100 − 10% of 100 = ₹90. Profit = 90 − 80 = ₹10 on CP ₹80. Profit% = 10/80 × 100 = 12.5%. Answer: 12.5%

SSC Pattern / Tips

• When the same article is sold at different profit/loss percentages to different customers at the same cost, compare total profits.
• For dishonest dealings (false weights), convert to price per kg equivalents to find effective gain%.
• In successive discount problems, first find the final SP from MP, then compare to CP for profit/loss.
• Watch for questions where discount% and profit% are the same number — this is a common pattern.

🔴 Extended

Full Concept

At the advanced Tier 2 level, profit/loss problems involve nested percentage changes, and the relationship between MP, CP, discount, and profit is formula-driven. The fundamental chain is:

CP → (Markup %) → MP → (Discount %) → SP → Compare with CP → Profit/Loss %

The markup percentage tells you how much above cost the seller initially priced the article. The discount percentage tells you how much the buyer actually pays below that initial price. These two percentages interact multiplicatively.

Key Identity: If an article is marked up by x% and then discounted by y%, the profit/loss% = (1 + x/100)(1 − y/100) − 1, all multiplied by 100.

False Weights (Dishonest Trading): This is a Tier 2 specialty. If a seller uses a weight of 900g but calls it 1kg, and buys at cost price but sells at cost price, his effective profit comes from selling 100g “free.” The gain% formula: Gain% = (True weight − False weight)/False weight × 100. If he also makes a profit of p% on his cost, then effective gain = p + G + pG/100.

Break-Even and Successive Profit/Loss: If an article is sold at successive profits of x%, y%, z%, the net result = (1 + x/100)(1 + y/100)(1 + z/100) − 1 × 100. This compounding approach applies to both profits and losses (use negative for loss).

Selling at Cost Price with Two Rate Transactions: If a seller sells at x% profit to one customer and y% loss to another from the same batch, and the selling prices are equal, find the combined profit/loss by equating total SP = total CP and using weighted average of ratios.

SSC CGL Deep Analysis

• Frequency: 1–2 questions per paper. Profit/loss combined with discount is common. False weight questions appear in Tier 2 nearly every alternate year.
• Difficulty: Medium. The false weight trick and successive percentage changes trip up 50%+ of test-takers.
• Recent trend: Questions combining markup + discount + overhead costs in a single scenario. Also, problems where a shopkeeper makes a profit x% when selling at discounted price but would make loss y% if he didn’t give the discount.
• Newer patterns: Finding the break-even point where discount equals profit percentage — if discount% = profit%, the seller neither gains nor loses overall (approximately).
• Total weight in Tier 2: Roughly 2–3% of the quant paper.

High-Scoring Strategy

1. Always draw the CP → MP → SP chain. Write what you know, solve step by step.
2. For false weight: effective CP per false kg = actual cost of true weight / false weight. Effective SP per false kg = selling price of claimed weight / false weight.
3. Use the net change formula for successive profits/losses instead of applying them one by one.
4. If question gives SP and gain%/loss%, always find CP first (SP × 100/(100 ± gain_loss)).
5. When two SPs are equal at different profit/loss%, find the CP ratio using inverse proportion: CP₁:CP₂ = (100 ∓ loss₂):(100 ± profit₁).

SSC-Level Practice

Q1: A merchant marks his goods at 40% above cost and gives a discount of 25%. Find his profit percent. Answer: 5% — Working: Let CP = 100. MP = 140. SP = 140 × 0.75 = 105. Profit = 5% on CP = 100.

Q2: A shopkeeper sells rice at ₹40/kg and makes a 25% profit. However, he uses a false weight of 800g for 1kg. Find his actual profit percent. Answer: 56.25% — Working: Cost of 800g = cost of 0.8kg at CP. He sells 800g at the price of 1000g. Effective SP per true kg = 40 × (1000/800) = 50. Effective profit = (50−40)/40 × 100 = 25%. Wait — with false weight alone: Gain% = (1000−800)/800 × 100 = 200/800 × 100 = 25%. Combined with 25% profit already: net = 25 + 25 + (25×25)/100 = 56.25%. Yes correct.

Common Traps

• Trap 1: Applying discount% to CP instead of MP. Discounts are always on the marked price.
• Trap 2: For false weight problems, using the wrong base for gain calculation. Gain% = extra quantity received / false quantity × 100, not extra / true quantity.
• Trap 3: Adding successive profit percentages instead of multiplying the multipliers. 20% + 20% is NOT 40% profit — it’s 44% (1.2 × 1.2 = 1.44).

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