Profit & Loss Questions for SSC CGL

Core Definitions & Relationships

Profit and Loss is fundamentally about comparing Cost Price (CP) and Selling Price (SP). When SP > CP, you make profit; when SP < CP, you incur loss. The key insight is that profit% and loss% are always calculated on the Cost Price unless the problem explicitly states otherwise. This is where many aspirants slip — they calculate on SP instead. Discount, on the other hand, is always calculated on the Marked Price (MP), not CP.

• Cost Price (CP) = what you pay to buy the item
• Selling Price (SP) = what you receive when you sell
• Marked Price (MP) = the price tag shown in the shop
• Profit = SP - CP; Loss = CP - SP
• Profit% and Loss% are ALWAYS on CP unless stated otherwise
• Discount% is ALWAYS on MP, not CP

Markup, Discount & Successive Changes

Markup is the difference between MP and CP. A shopkeeper marks up goods to allow room for discount while still making profit. When multiple discounts are applied (e.g., 10% then 5%), you cannot add them — you must apply them sequentially. Similarly, if profit% and discount% are both involved, work step by step: first find SP from profit%, then apply discount to find final SP. Successive percentage changes multiply, not add.

• Markup = MP - CP; Markup% = (MP - CP) / CP × 100
• Multiple discounts: apply one after another, not cumulatively
• Two successive discounts of a% and b% = single equivalent discount of [a + b - (a×b)/100]%
• When profit% and discount% both exist: CP → (apply profit%) → MP → (apply discount%) → SP
• Always identify what the percentages are calculated on before solving

Tricky Scenarios: Faulty Weights, Mixing, & Transactions

SSC CGL loves to test P&L in disguised scenarios. A shopkeeper using faulty weights is essentially changing the effective CP or SP. If a shopkeeper claims to sell at cost but uses faulty weights, they are actually making profit. Similarly, mixing two items at different costs and selling at a blended rate requires weighted average thinking. Multiple buy-sell transactions need careful tracking of total CP and total SP.

• Faulty weights: if seller gives less weight, effective CP decreases (profit increases)
• Mixing problem: use weighted average; profit/loss on mixture = weighted average SP - weighted average CP
• Dishonest seller: profit% = (true weight / false weight - 1) × 100 when selling at cost
• Multiple transactions: sum all CPs, sum all SPs, then calculate overall profit/loss
• Read carefully: 'cost price' vs 'marked price' vs 'selling price' — they are different

Percentage Chain & Reverse Calculations

Sometimes you are given final SP and asked to find CP or profit%. This requires reversing the formula. If SP = CP × (100 + Profit%) / 100, then CP = SP × 100 / (100 + Profit%). Percentage chains occur when multiple operations happen in sequence — apply them in order, not in reverse. A common trap: students try to reverse a discount by adding instead of multiplying.

• Reverse formula: CP = SP × 100 / (100 + Profit%)
• Reverse loss: CP = SP × 100 / (100 - Loss%)
• Reverse discount: MP = SP × 100 / (100 - Discount%)
• Chain of operations: apply sequentially, not in reverse
• If profit% increases by 10%, it does NOT mean multiply by 1.1 — recalculate from scratch

• Calculating profit% on SP instead of CP — always use CP as the base unless explicitly told otherwise
• Adding multiple discounts instead of applying them sequentially — 10% + 5% is NOT 15%, it is 14.5%
• Confusing Marked Price with Cost Price — MP is what is written on the tag, CP is what the shopkeeper paid
• Forgetting to apply discount after calculating profit — if both profit% and discount% are given, profit% is on CP→MP, then discount% is on MP→SP
• Misreading 'at cost' — if a seller claims to sell at cost but uses faulty weights, they are actually profiting; do not assume zero profit

• CMP Rule: Cost Price, Marked Price, Profit% on CP, Discount% on MP — remember the order and what each percentage applies to
• Reverse Flip: If SP = CP × (100 + P%) / 100, then CP = SP × 100 / (100 + P%) — flip the fraction and swap the roles
• Successive Discount Formula: a + b - ab/100 — think of it as 'add them, subtract their overlap'
• Faulty Weight Trick: Profit% = (true weight / false weight - 1) × 100 — the ratio of weights gives the profit directly

• SSC CGL Tier 1 typically has 1-2 straightforward P&L questions (CP→SP or discount calculation); Tier 2 has 2-4 questions, often with twists like faulty weights or successive discounts
• Time management: basic P&L questions should take 1-2 minutes max; if you are stuck, skip and return — these are not the hardest quant topics
• Watch for percentage chain questions in recent papers (2022-2024) — they test your ability to reverse formulas and work backwards from SP to CP
• Mixing and faulty weight problems are increasing in frequency; practice these scenarios specifically — they often appear in Tier 2
• Always double-check your base: is the percentage on CP, MP, or SP? Misidentifying this causes 90% of errors in this topic