Profit Loss Discount Basic Transactions Questions for UP POLICE CONSTABLE

Cost Price, Selling Price, Profit, Loss

Cost Price (CP) is what the shopkeeper pays to buy goods. Selling Price (SP) is what the customer pays. If SP > CP, there is Profit. If SP < CP, there is Loss. Profit or Loss is always calculated as a percentage of Cost Price, not Selling Price. This is the most common error—students calculate percentage on SP instead of CP and get wrong answers.

• Profit = SP - CP (in rupees)
• Loss = CP - SP (in rupees)
• Profit % = (Profit / CP) × 100
• Loss % = (Loss / CP) × 100
• SP = CP + Profit OR SP = CP - Loss
• Always use CP as the base for percentage calculation

Marked Price and Discount

Marked Price (MP) is the price printed on the tag—the list price. Discount is a reduction given on MP. The customer pays Selling Price = MP - Discount. Discount is always calculated on Marked Price, not Cost Price. A shopkeeper can give discount while still making profit if MP > CP.

• Discount = MP - SP (in rupees)
• Discount% = (Discount / MP) × 100
• SP = MP - Discount OR SP = MP × (1 - Discount%/100)
• Discount is given on MP, not CP
• Profit/Loss is calculated on CP, not MP
• A shopkeeper can profit even after giving discount if MP > CP

Successive Discounts

When two or more discounts are given one after another, they are called successive discounts. The second discount is applied on the price after the first discount, not on the original MP. A common trap: students add discounts (10% + 20% = 30%) but this is wrong. Successive discounts are multiplicative, not additive.

• Successive discounts are applied one after another
• Do NOT add successive discounts
• If discounts are d1% and d2%, final SP = MP × (1 - d1/100) × (1 - d2/100)
• Equivalent single discount = 100 - (final SP/MP × 100)
• Example: 10% and 20% successive discounts ≠ 30% single discount

Profit/Loss with Marked Price

In real exams, questions often mix all three concepts: CP, MP, and SP. A shopkeeper marks goods above CP to allow room for discount while still making profit. The relationship is: CP → MP (marked up) → SP (after discount). You must track all three separately and not confuse which percentage applies to which base.

• Markup% = ((MP - CP) / CP) × 100
• Profit% is always on CP, discount% is always on MP
• SP determines profit/loss: if SP > CP, profit; if SP < CP, loss
• A shopkeeper can give discount and still profit if MP > CP
• Read the question carefully: which price is given, which is asked

• Calculating profit/loss percentage on SP instead of CP. Remember: profit% = (profit/CP) × 100, NOT (profit/SP) × 100.
• Adding successive discounts instead of multiplying. 10% + 20% discount does NOT equal 30% discount. Use multiplication: 0.9 × 0.8 = 0.72, so 28% equivalent discount.
• Confusing which price is the base for percentage. Profit% uses CP as base, discount% uses MP as base. Read carefully.
• Forgetting that discount is on MP, not CP. A shopkeeper marks above CP to allow discount room. Don't mix up the three prices.
• Careless arithmetic in mental math. These questions are easy but time-pressure causes sign errors and calculation mistakes. Double-check your final answer.

• CPM-SPD: Cost Price is the base for profit/loss Percentage. Marked Price is the base for Discount percentage.
• PROFIT RULE: SP > CP = Profit. SP < CP = Loss. Profit% = (SP - CP)/CP × 100. Always divide by CP.
• DISCOUNT RULE: Discount% = (MP - SP)/MP × 100. Always divide by MP, not CP.
• SUCCESSIVE DISCOUNT: Multiply, don't add. If 20% and 10%, calculate as 0.8 × 0.9 = 0.72, meaning 28% total discount.

• UP Police Constable typically asks 2-3 profit-loss-discount questions. Most are straightforward single-concept questions, but 1 may mix CP, MP, and SP together.
• Time pressure is real: these questions should take 1-2 minutes each. Pre-calculate common percentages (10%, 20%, 25%, 33.33%) to avoid long division.
• Recent papers show preference for questions with MP and discount given, asking for profit%. Practice this pattern: CP given → MP given → discount% given → find profit%.
• Watch for 'marked price' vs 'cost price' language. Hindi papers sometimes use 'ankita mulya' (marked price) and 'khareed mulya' (cost price). Know both terms.
• Successive discount questions are less common but high-value if you know the trick. If you see two discounts mentioned, immediately think multiplication, not addition.