Percentage Profit-Loss and Discount Questions for UPSC CSE

Core Definitions

Cost Price (CP) is what you pay to get the item. Selling Price (SP) is what the buyer pays you. Marked Price (MP) is the printed tag price before discount. Discount is always calculated on MP, while Profit or Loss is always calculated on CP. Confusing these two bases is the single biggest trap in this topic.

• Profit = SP - CP (when SP > CP)
• Loss = CP - SP (when CP > SP)
• Profit% = (Profit / CP) x 100
• Loss% = (Loss / CP) x 100
• Discount = MP - SP
• Discount% = (Discount / MP) x 100

Successive Discounts and Effective Price

When two discounts d1% and d2% are applied one after the other, they do NOT simply add up. The second discount applies on the already-reduced price. The single equivalent discount formula saves time in the exam. Think of it like two tax deductions applied on a shrinking base.

• Effective single discount = d1 + d2 - (d1 x d2)/100
• A discount of 20% then 10% is NOT 30%. It equals 28%.
• Always apply percentage on the current value, not original
• For three successive discounts, apply the formula twice
• Successive discounts of the same value always give less than double that discount

Profit-Loss with Faulty Weights

A classic UPSC CSAT twist: a shopkeeper claims to sell at cost price but uses a faulty weight (say 900 g instead of 1000 g). This creates a hidden profit. The logic is simple — the shopkeeper gives less but charges for more. The profit% is calculated on actual quantity given, not claimed quantity.

• Profit% = (Error / True Value - Error) x 100
• Error = True weight minus Faulty weight
• If selling at CP with 900g weight instead of 1000g: Profit% = 100/900 x 100 = 11.11%
• If selling at a discount as well as using faulty weights, calculate both effects separately then combine

Combined MP-Discount-Profit Problems

UPSC loves questions that link all three: MP, discount, CP and profit together. The chain is: Start at MP, apply discount to get SP, then compare SP with CP to find profit/loss. You are often given two of the four values and asked to find the third or fourth. Always write out MP, CP, SP, D%, P% as a table before solving.

• SP connects MP side (via discount) and CP side (via profit/loss)
• SP = MP x (100-D%)/100 = CP x (100+P%)/100
• This double-equation lets you find any unknown if two values are given
• If MP is x% above CP, and discount is d%, net profit% = (100+x)(100-d)/100 - 100
• Markup and discount are not the same thing — markup is on CP, discount is on MP

Percentage Change Basics

Many profit-loss questions are essentially percentage change questions in disguise. Remember: percentage change is always calculated on the original/base value, not the new value. A 25% increase followed by a 20% decrease does not return you to the original — you land at 100%.

• Percentage Change = (New - Old) / Old x 100
• A 20% rise then 20% fall gives net change of -4%, not 0
• To increase by 25%, multiply by 5/4. To decrease by 20%, multiply by 4/5
• These fraction shortcuts are faster than doing decimal arithmetic in exam
• Net multiplier for two successive changes = (1 + r1/100)(1 + r2/100)

• Calculating discount% on CP instead of MP — discount is always on the Marked Price, never on Cost Price.
• Adding two successive discounts directly (e.g., treating 20% + 10% as 30%) — they are never additive because the second applies on a reduced base.
• Calculating profit% on SP instead of CP — profit and loss percentages are ALWAYS on Cost Price.
• In faulty weight problems, dividing the error by the true weight instead of the false weight — the formula uses false weight in the denominator.
• Confusing markup (on CP) with discount (on MP) in combined problems, leading to wrong equation setup.

• DAMPS rule: Discount on MP, All profit/loss on SP-CP comparison, Markup on CP, Percentage always on base. Remembering what is the BASE for each calculation prevents all major errors.
• The chain arrow: CP → (markup up) → MP → (discount down) → SP → (compare back to CP for profit/loss). Draw this arrow in rough work for every combined question.
• Successive discount shortcut: think of two tax cuts on a salary. First cut reduces the base, second cut hits the smaller base. They never add up to a simple sum.
• Fraction shortcut table: 10%=1/10, 20%=1/5, 25%=1/4, 33.3%=1/3, 50%=1/2. Convert percentages to fractions immediately to avoid decimal errors in exam.

• CSAT 2023 and 2022 both had at least two profit-loss questions. One was straightforward SP/CP, one involved a twist (faulty weights or successive discounts). Expect this pattern.
• Since CSAT is qualifying at 33%, do not spend more than 90 seconds per question here. If a question involves more than two unknowns, mark and move — come back if time allows.
• Assumption of CP = 100 is the fastest trick. Set CP = 100 in any question where only percentages are given. This converts abstract percentages into concrete numbers instantly.
• Watch for the word 'on' — profit of 20% ON cost price vs discount of 10% ON marked price. Underlining ON in the question during reading time prevents base confusion.
• Questions sometimes hide profit-loss inside ratio problems. If two traders buy at the same price and one sells at 10% profit and the other at 15% loss, set CP = 100 and compute SPs to find their ratio directly.