Profit and Loss: Concepts and Problems Solved Under 1 Min

Profit and loss appears in TCS NQT, Infosys InfyTQ, AMCAT, and most major campus placement aptitude tests; every examiner tests the same three formula categories.

Core Definitions: CP, SP, Profit, and Loss

Every profit-and-loss problem starts with two prices:

• Cost Price (CP): what the trader paid to acquire or produce the goods.
• Selling Price (SP): the price at which the trader sells to the buyer.

The trade result depends on which is larger:

• If SP is greater than CP: Profit = SP − CP
• If SP is less than CP: Loss = CP − SP
• If SP equals CP: no profit, no loss

These absolute rupee figures are not enough to compare two transactions. A higher absolute profit does not always signal a better trade: the return on investment is what counts.

Profit Percentage and Loss Percentage

The most tested concept, and the top source of errors, is the base for percentage calculations.

Profit% = (Profit / CP) × 100

Loss% = (Loss / CP) × 100

The base is always CP. Never SP.

Margin is a related but distinct figure: profit expressed as a percentage of SP rather than CP.

• Margin = (Profit / SP) × 100

For the same transaction, margin is always smaller than profit%. Taking a small numerical example:

• Trader buys at ₹15, sells at ₹16 (profit = ₹1)
• Profit% = 1/15 × 100 = 6.67%
• Margin = 1/16 × 100 = 6.25%

When a placement question gives a percentage figure without specifying the base, assume CP unless the word “margin” appears explicitly.

Reverse-lookup formulas (for when CP or SP is the unknown):

• CP = SP × 100 / (100 + P%) when profit% is known
• CP = SP × 100 / (100 − L%) when loss% is known
• SP = CP × (100 + P%) / 100
• SP = CP × (100 − L%) / 100

These formulas appear directly in questions of the form: “sold at ₹X for a profit/loss of Y%, find CP.”

Marked Price, Discount, and Successive Discounts

Retail problems add a third price: the Marked Price (MP), the price printed or tagged on the item. A discount is offered on the MP:

• Discount = MP − SP
• Discount% = (Discount / MP) × 100
• SP = MP × (1 − d/100)

Profit is still measured from CP to SP, not from MP to SP. A common error is computing profit on the marked price.

Successive discounts apply when two or more discounts reduce the price in stages. Two discounts of d1% and d2% do not add up to (d1 + d2)%. The correct formula:

Net discount = d1 + d2 − (d1 × d2) / 100

This follows from SP = MP × (1 − d1/100) × (1 − d2/100). Expanding gives the cross-term (d1 × d2)/100, which is the correction that makes successive discounts smaller than their naive sum.

Time-and-work and other quantitative aptitude topics that appear alongside profit-loss in the same test use the same percentage-based reasoning.

The Dishonest-Shopkeeper Problem Type

A frequent placement question type: a seller uses a false weight but charges for the full amount. The formula:

• Profit% = (True weight − False weight) / False weight × 100

This is derived by treating the seller’s actual CP as based on the false (lower) weight dispensed, while the SP is based on the full (true) weight billed. Two worked examples:

• Seller claims to give 1 kg but dispenses 900 g: profit% = (1000 − 900) / 900 × 100 = 11.11%
• Seller claims to give 1000 g but dispenses 800 g: profit% = (1000 − 800) / 800 × 100 = 25%

The denominator is always the false weight (what the seller actually hands over), not the claimed weight.

Speed Tricks: Formula Reference

The six formulas below cover the bulk of profit-loss variants in campus placement tests:

• CP from SP + profit%: CP = SP × 100 / (100 + P%)
• CP from SP + loss%: CP = SP × 100 / (100 − L%)
• SP from CP + profit%: SP = CP × (100 + P%) / 100
• SP from CP + loss%: SP = CP × (100 − L%) / 100
• Successive discounts: net discount = d1 + d2 − (d1 × d2) / 100
• Dishonest shopkeeper: profit% = (error in weight / false weight) × 100

The NCERT Class 8 Mathematics chapter on Comparing Quantities derives all of these from first principles. Placement aptitude tests rarely go beyond this level for the profit-loss topic.

Solved Problems, Step by Step

All examples re-derived from first principles.

• Q1: A trader buys goods at ₹500 and sells at ₹450. Find loss%.

  • Loss = 500 − 450 = 50
  • Loss% = 50 / 500 × 100 = 10%
  • Answer: 10% loss

• Q2: Article sold at 7% loss. Selling at ₹100 more gives 13% profit. Find CP.

  • SP1 = CP × 93/100; SP2 = CP × 113/100
  • SP2 − SP1 = 100, so CP × (113 − 93) / 100 = 100, giving CP × 20/100 = 100
  • CP = 500
  • Answer: ₹500

• Q3: Article sold at ₹423 = 10% loss. What SP gives 10% profit?

  • CP = 423 × 100/90 = 470
  • SP for 10% profit = 470 × 110/100 = 517
  • Answer: ₹517

• Q4: Man gains 10% at current SP. SP increased by 50%. New profit%?

  • Let CP = 100; original SP = 110
  • New SP = 110 × 150/100 = 165
  • New profit = 165 − 100 = 65; profit% = 65/100 × 100 = 65%
  • Answer: 65%

• Q5: Profit at ₹1060 is 20% more than loss at ₹950. Find CP.

  • Profit = 1060 − CP; Loss = CP − 950
  • Equation: 1060 − CP = 1.2 × (CP − 950)
  • 1060 − CP = 1.2CP − 1140; so 2200 = 2.2CP; CP = 1000
  • Answer: ₹1000

• Q6: CP is 25% less than SP. Find profit%.

  • CP = SP − 25% of SP = 0.75SP, so SP = CP / 0.75 = CP × 4/3
  • Profit = SP − CP = CP/3
  • Profit% = (CP/3) / CP × 100 = 33.33%
  • Answer: 33.33%

• Q7: Amit sells his watch for ₹200 at 20% profit. Find CP.

  • SP = CP × (100 + 20) / 100, so 200 = CP × 120/100
  • CP = 200 × 100/120 = 166.67
  • Answer: ₹166.67

• Q8: Ramesh sells a watch at ₹100, incurring an absolute loss of ₹10. Find loss%.

  • CP = SP + absolute loss = 100 + 10 = 110
  • Loss% = 10 / 110 × 100 = 9.09%
  • Answer: 9.09% (not 10%: the base is CP = 110, not SP = 100)

• Q9: Shopkeeper marks goods 25% above CP, then offers 10% discount. Find profit%.

  • Let CP = 100; MP = 125; SP = 125 × 90/100 = 112.50
  • Profit% = (112.50 − 100) / 100 × 100 = 12.5%
  • Answer: 12.5%

• Q10: Two successive discounts of 20% and 10% on a ₹500 marked-price item. Find SP.

  • SP = 500 × (80/100) × (90/100) = 500 × 0.72 = 360
  • Net discount check: 20 + 10 − (20 × 10)/100 = 28%, and 500 × 72/100 = 360
  • Answer: ₹360

The Mu Sigma aptitude test (MuApt) includes profit-loss and percentage problems as a consistent part of its quant section. The campus placement evaluation test quant section routinely features problems at the Q3 and Q5 level of complexity.

For more practice at placement-test difficulty, IndiaBix’s profit and loss set has 100-plus problems with answer keys.

Once the profit-loss formula is second nature, companies have started testing data interpretation that applies the same percentage reasoning to real-world performance data. TinkerLLM extends that skill to AI tool evaluation at ₹299: the platform connects percentage math to how models measure accuracy scores and cost-per-query tradeoffs.