Profit and Loss Questions for UP POLICE CONSTABLE

Core Definitions and Formulas

Profit and Loss revolves around three prices: Cost Price (CP) is what you buy for, Selling Price (SP) is what you sell for, and Marked Price (MP) is the tag price before discount. Profit happens when SP > CP; Loss when SP < CP. The key insight is that profit % and loss % are ALWAYS calculated on Cost Price unless the question explicitly says otherwise. Discount % is calculated on Marked Price. This distinction is where most errors occur.

• Profit = SP - CP; Loss = CP - SP
• Profit % = (Profit / CP) × 100; Loss % = (Loss / CP) × 100
• Discount % = (Discount / MP) × 100, where Discount = MP - SP
• SP = CP + Profit OR SP = CP × (100 + Profit%) / 100
• SP = CP - Loss OR SP = CP × (100 - Loss%) / 100
• SP = MP - Discount OR SP = MP × (100 - Discount%) / 100

Marked Price, Discount, and Successive Discounts

Marked Price (MP) is the list price shown on the tag. Shopkeepers mark up goods above cost price to allow room for discount while still making profit. When multiple discounts are applied one after another (like 10% then 20%), you cannot simply add them; you must apply them sequentially. This is called successive discounts. The formula for two successive discounts is: Final SP = MP × (100 - D1) / 100 × (100 - D2) / 100.

• Markup = MP - CP; Markup % = (Markup / CP) × 100
• Discount is always on Marked Price, not Cost Price
• For successive discounts, apply one after the other; do NOT add percentages
• Equivalent single discount for D1 and D2: D_eq = D1 + D2 - (D1 × D2) / 100
• If profit % and discount % are given, use: SP = CP × (100 + Profit%) / 100 and SP = MP × (100 - Discount%) / 100, then equate

Profit and Loss with Quantity and Mixtures

Sometimes questions involve buying and selling multiple items, or mixing items at different costs. The key is to calculate total CP and total SP, then find overall profit or loss. If items are sold at different profit %s, you must track each separately or use weighted averages. Be careful: if 10 items are bought at Rs 5 each and 15 items at Rs 8 each, total CP = 10×5 + 15×8 = 50 + 120 = Rs 170.

• Total CP = sum of (quantity × unit cost) for all batches
• Total SP = sum of (quantity × unit selling price) for all batches
• Overall Profit % = ((Total SP - Total CP) / Total CP) × 100
• When items are mixed, calculate total CP and total SP first, then profit %
• Be alert: profit % on different items may differ; always use total figures for overall %

False Weight and Adulteration (Common in UP Police)

UP Police exams often include profit-loss questions disguised as false weight problems. A shopkeeper claims to sell at cost price but uses false weights (e.g., gives 900g instead of 1000g). This creates hidden profit. The formula: if he claims to give W1 but gives W2, his profit % = ((W1 - W2) / W2) × 100. Similarly, if he mixes cheaper items with expensive ones, the profit is the difference in cost weighted by quantity.

• False weight profit % = ((Claimed weight - Actual weight) / Actual weight) × 100
• If shopkeeper claims to sell at cost price but uses false weights, profit = false weight profit %
• Adulteration: if pure item costs Rs X per kg and adulterant costs Rs Y per kg, profit from mixing depends on ratio
• Always identify: what is claimed vs. what is actual

• Calculating profit % on Selling Price instead of Cost Price. Remember: profit % is ALWAYS on CP unless stated otherwise. If SP = 120 and profit = 20, CP = 100, profit % = 20%, NOT 20/120 × 100 = 16.67%.
• Adding successive discounts instead of multiplying. If two 20% discounts are applied, final price is NOT 60% of MP; it is 80% × 80% = 64% of MP.
• Confusing Marked Price with Cost Price. Discount is on MP, not CP. If MP = 1000, CP = 600, discount = 10%, then SP = 900, and profit = 300, profit % = 50%, NOT based on discount.
• Forgetting to convert percentages to decimals. Always use (100 + Profit%) / 100 or (100 - Loss%) / 100 in formulas, not just the percentage number.
• In false weight problems, using claimed weight as denominator instead of actual weight. Profit % = ((Claimed - Actual) / Actual) × 100, not / Claimed.

• CP-SP-MP Triangle: CP is base (cost), SP is middle (selling), MP is top (marked/tag). Profit/Loss measured from CP. Discount measured from MP.
• PROFIT = SP > CP; LOSS = SP < CP. Think: Profit is when you sell Higher than you bought.
• Successive Discount Multiply Rule: D1 then D2 means multiply (1 - D1/100) × (1 - D2/100), NOT add. Example: 20% then 10% = 0.8 × 0.9 = 0.72 = 28% equivalent single discount.
• False Weight Trick: If you claim to give 1000g but give 900g at cost price, you're actually making profit = 1000/900 - 1 = 11.11%. The 'extra' 100g is free profit.

• UP Police Constable typically includes 2-3 profit-loss questions in the 60-minute quant section. They are usually straightforward (not tricky) if you know formulas; expect 1 easy, 1 medium, 1 hard.
• False weight and adulteration questions are VERY common in UP Police. If you see a question about 'selling at cost price' but with a twist (false weights, mixing), immediately think hidden profit.
• Successive discount questions appear frequently. Practice the equivalent single discount formula; it saves time and avoids calculation errors.
• Watch for questions that mix profit % with discount %. These require you to set up two equations: SP from profit side and SP from discount side, then solve for unknown (usually CP or MP).
• Time management: Profit-loss questions should take 1.5-2 minutes max. If you're stuck, skip and return. Most questions follow standard patterns; if it looks unfamiliar, re-read carefully—it's likely a false weight or adulteration variant.