Profit Loss Discount Basic Transactions Questions for BIHAR POLICE CONSTABLE

Core Definitions and Relationships

Profit and Loss are calculated on Cost Price (CP). Discount is always on Marked Price (MP). Think of it like this: a shopkeeper buys goods at CP, marks them at MP (to earn profit), then gives discount to attract customers, and finally sells at SP. The three prices are separate — don't confuse them. Profit happens when SP > CP. Loss happens when SP < CP.

• Cost Price (CP) = what shopkeeper pays to buy the item
• Marked Price (MP) = price written on the tag (before discount)
• Selling Price (SP) = final price customer pays
• Profit = SP - CP (only positive means profit)
• Loss = CP - SP (only positive means loss)
• Discount = MP - SP (reduction from marked price)

Profit and Loss Percentage Formulas

Profit% and Loss% are always calculated on Cost Price, not Selling Price. This is the most common mistake. If you buy a pen for Rs 10 and sell for Rs 12, profit is Rs 2, but profit% is 20% (of the CP=10), not 16.67% (of SP=12). Remember: percentage is always relative to the base you started with, which is CP.

• Profit% = (Profit / CP) × 100
• Loss% = (Loss / CP) × 100
• SP = CP + Profit, so SP = CP(1 + Profit%/100)
• SP = CP - Loss, so SP = CP(1 - Loss%/100)
• If Profit% is given, you can find SP directly without calculating profit amount first

Discount Percentage Formula

Discount is ALWAYS calculated on Marked Price (MP), not Cost Price or Selling Price. This is critical. A shopkeeper marks an item at Rs 1000 and gives 20% discount. The discount amount is 200 (20% of 1000), so SP becomes 800. Many students mistakenly calculate discount on CP or SP — this is wrong. Discount% = (Discount Amount / MP) × 100.

• Discount = MP - SP
• Discount% = (Discount / MP) × 100
• SP = MP × (100 - Discount%) / 100
• MP = SP × 100 / (100 - Discount%)
• Discount% and Profit% are independent — both can exist in same transaction

Combined Profit-Loss-Discount Transactions

Real exam questions mix all three concepts. A shopkeeper buys at CP, marks at MP (to earn profit), gives discount, and sells at SP. You need to track all three prices. The profit% is always calculated on CP (the original cost), not on MP. Work step-by-step: first find SP from discount, then find profit/loss from CP and SP.

• Step 1: Find SP from MP and Discount% using SP = MP × (100 - Discount%)/100
• Step 2: Compare SP with CP to find profit or loss
• Step 3: Calculate Profit% or Loss% using CP as base
• Profit% on CP = ((SP - CP) / CP) × 100, not ((SP - MP) / MP) × 100
• Markup% (MP vs CP) is different from Profit% (SP vs CP)

• Calculating Profit% or Loss% on SP instead of CP. Remember: profit/loss is YOUR gain/loss relative to what YOU paid (CP), not relative to selling price.
• Calculating Discount% on CP or SP instead of MP. Discount is always a reduction from the marked/tagged price, never from cost or selling price.
• Confusing Markup% with Profit%. Markup is (MP-CP)/CP × 100. Profit% is (SP-CP)/CP × 100. They are different because MP ≠ SP when discount is given.
• Forgetting to convert percentage to decimal form. If Profit% = 25%, then SP = CP × 1.25, not CP × 25. Use (100 + Profit%)/100 as multiplier.
• In multi-step problems, losing track of which price you're using. Always label: CP, MP, SP clearly and update as you solve.

• CP-MP-SP order: Cost Price is what you Pay, Marked Price is what's written, Selling Price is what customer pays. Think: P-W-C (Pay-Written-Customer).
• Profit% and Loss% use CP as base — remember 'P for Profit, P for Price (Cost Price)' — both start with P.
• Discount% uses MP as base — remember 'D for Discount, D for Display price (Marked Price)' — both start with D.
• Formula shortcut: SP = CP × (100 ± Profit%)/100 and SP = MP × (100 - Discount%)/100. The ± depends on profit (plus) or loss (minus).

• Bihar Police Constable typically asks 3-4 questions on this topic per paper. Usually 1 straightforward profit/loss question, 1 discount question, and 1-2 combined questions.
• Time management: Each question should take 1-2 minutes max. Use the direct SP formulas instead of calculating intermediate profit/loss amounts — saves time.
• Recent papers show preference for 'find CP given SP and Profit%' or 'find MP given SP and Discount%' reverse-calculation questions. Practice rearranging formulas.
• Watch for percentage traps: a 50% profit followed by 50% loss does NOT return you to original price. Always recalculate step-by-step.
• Decimal/fraction conversions are common: 20% = 1/5, 25% = 1/4, 33.33% = 1/3. Knowing these speeds up mental math significantly in exam.