Profit, Loss and Discount
Overview
Profit, Loss and Discount forms a cornerstone of commercial mathematics and appears consistently in HSSC CET's Quantitative Ability section. These problems test your understanding of everyday business transactions—buying, selling, calculating margins, and offering discounts. The topic connects directly to real-life scenarios, making it both practical and exam-relevant.
For CET, you must master the relationship between Cost Price (CP), Selling Price (SP), Marked Price (MP), and how discounts affect final selling prices. Questions typically involve calculating profit or loss percentages, finding CP or SP when percentage is given, successive discounts, and dishonest dealer problems. Most questions are straightforward formula applications, but some require careful reading to identify what's actually being asked.
Strong command of percentages is essential here since profit, loss, and discount are always expressed as percentages of specific base values. Students who confuse the base (CP vs SP vs MP) lose easy marks.
Key Concepts
- Cost Price (CP) is the price at which a trader buys goods. This is the base for calculating profit or loss percentage.
- Selling Price (SP) is the price at which a trader sells goods to a customer. Comparing SP with CP determines profit or loss.
- Marked Price (MP) is the price labelled on the product (also called List Price or Catalogue Price). Discounts are calculated on MP, not CP.
- Profit occurs when SP > CP; Loss occurs when SP < CP. The difference gives the absolute profit or loss.
- Discount is the reduction offered on Marked Price to arrive at the Selling Price. Discount = MP − SP.
- Successive discounts are applied one after another on the reduced price, not on the original MP.
- The base matters: Profit/Loss percentage is always on CP. Discount percentage is always on MP.
- Break-even means SP = CP, i.e., no profit no loss.
Formulas / Key Facts
Basic Formulas:
- Profit = SP − CP
- Loss = CP − SP
- Profit % = (Profit / CP) × 100
- Loss % = (Loss / CP) × 100
Finding SP from CP:
- When profit: SP = CP × (100 + Profit%) / 100
- When loss: SP = CP × (100 − Loss%) / 100
Finding CP from SP:
- When profit: CP = SP × 100 / (100 + Profit%)
- When loss: CP = SP × 100 / (100 − Loss%)
Discount Formulas:
- Discount = MP − SP
- Discount % = (Discount / MP) × 100
- SP = MP × (100 − Discount%) / 100
Successive Discounts:
- For discounts of a% and b%, equivalent single discount = a + b − (ab/100) %
Relation between MP, CP, Profit and Discount:
- If a trader marks goods x% above CP and gives y% discount:
- Profit or Loss % = x − y − (xy/100)
- Positive result means profit; negative means loss.
Dishonest Dealer (using false weights):
- Profit % = (True weight − False weight) / False weight × 100
- Or: Gain % = (Error / True value − Error) × 100
Worked Examples
Example 1: Basic Profit Calculation
A shopkeeper buys a watch for ₹800 and sells it for ₹920. Find the profit percentage.
Solution:
- CP = ₹800, SP = ₹920
- Profit = 920 − 800 = ₹120
- Profit % = (120 / 800) × 100 = 15%
Answer: 15% profit
Example 2: Marked Price with Discount
A shirt is marked at ₹1,250. A shopkeeper offers 20% discount and still makes 25% profit. Find the Cost Price.
Solution:
- MP = ₹1,250, Discount = 20%
- SP = 1250 × (100 − 20) / 100 = 1250 × 80/100 = ₹1,000
- Profit = 25%, so CP = SP × 100 / (100 + 25)
- CP = 1000 × 100 / 125 = ₹800
Answer: CP = ₹800
Example 3: Successive Discounts
Two successive discounts of 20% and 10% are offered on an article marked at ₹500. Find the final selling price and equivalent single discount.
Solution:
- After first discount: 500 × (80/100) = ₹400
- After second discount: 400 × (90/100) = ₹360
- Final SP = ₹360
Equivalent single discount = 20 + 10 − (20×10/100) = 30 − 2 = 28%
Verification: 500 × (72/100) = ₹360 ✓
Answer: SP = ₹360, Equivalent discount = 28%
Example 4: Dishonest Dealer
A dishonest shopkeeper claims to sell at cost price but uses a weight of 900 grams instead of 1 kg. Find his gain percentage.
Solution:
- He gives 900 g but charges for 1000 g
- Gain = 1000 − 900 = 100 g
- Gain % = (100 / 900) × 100 = 100/9 = 11.11% (or 11⅑%)
Answer: 11⅑% or approximately 11.11%
Common Mistakes
- Calculating profit % on SP instead of CP → Always remember: Profit and Loss percentages are calculated on Cost Price, not Selling Price.
- Applying successive discounts on original MP → Each successive discount applies to the reduced price after the previous discount, not the original marked price.
- Confusing discount percentage with profit percentage → Discount is on MP while profit/loss is on CP. A 20% discount does not mean 20% loss.
- Forgetting the cross-term in successive discount formula → For discounts a% and b%, the equivalent is NOT simply (a + b)%. You must subtract ab/100.
- In dishonest dealer problems, using wrong base → The gain percentage is calculated on what the dealer actually gives (false weight), not what he claims (true weight).
- Not reading whether question asks for CP, SP, or percentage → Many students calculate correctly but answer the wrong quantity.
Quick Reference
- Profit/Loss % is always calculated on Cost Price.
- Discount % is always calculated on Marked Price.
- SP = CP × (100 ± Profit/Loss%) / 100
- Two successive discounts a% and b% = (a + b − ab/100)%
- Dishonest dealer gain = (Error / Actual quantity given) × 100
- If marked up by x% and discount y%, net effect = x − y − xy/100