Profit and Loss word problems become easier when you translate the language into CP, SP, MP, profit, loss and discount before doing any arithmetic. The arithmetic itself is often simple; the real challenge is identifying which value each sentence represents and which percentage base the question is using.
This guide focuses on the language patterns used in SSC, Banking and Railway exams. The method is simple: convert words into symbols, identify the base, write the relation and only then calculate.
1. The Words-to-Symbols Method
Before solving, translate common phrases:
- Bought for / purchased for / cost him → CP
- Sold for / sells at / realised → SP
- Marked at / list price / printed price → MP
- Gains / earns profit → SP is above CP
- Loses / sold at a loss → SP is below CP
- Discount of → percentage normally applies to MP
This translation step prevents most word-problem mistakes.
2. Direct Buying and Selling Language
Example: A trader buys an article for ₹400 and sells it for ₹460.
CP = ₹400, SP = ₹460, so profit = ₹60.
Profit% = 60 ÷ 400 × 100 = 15%.
3. Loss Wording
Example: A shopkeeper purchases an item for ₹800 and sells it at a loss of 15%.
SP = 800 × 85/100 = ₹680.
The phrase “15% loss” means SP is 85% of CP.
4. Marked Price and Discount Language
Example: A watch is marked at ₹900 and sold at a discount of 10%.
MP = ₹900. Customer pays 90% of MP.
SP = 900 × 90/100 = ₹810.
If CP = ₹720, profit = ₹90 and profit% = 90/720 × 100 = 12.5%.
For deeper MP-SP questions, use Discount and Marked Price Questions.
5. “After Giving Discount, Still Earns Profit” Pattern
Example: A seller marks an article at ₹1,500, gives 20% discount and still earns 20% profit.
First find SP:
SP = 1,500 × 80/100 = ₹1,200.
Since ₹1,200 is 120% of CP:
CP = 1,200 × 100/120 = ₹1,000.
Always follow MP → discount → SP → compare with CP.
6. Reverse Profit Wording
Example: An article is sold for ₹720 at 20% profit. Find its cost price.
₹720 represents 120% of CP.
CP = 720 × 100/120 = ₹600.
Do not subtract 20% of ₹720 directly.
7. Reverse Loss Wording
Example: An article is sold for ₹680 at 15% loss.
SP is 85% of CP.
CP = 680 × 100/85 = ₹800.
8. “More Than” and “Less Than” Base Trap
If A is 25% more than B, take B = 100, so A = 125.
Now B is 25/125 × 100 = 20% less than A.
The reverse percentage is different because the base changes.
9. Markup Followed by Discount
Example: A shopkeeper marks an article 25% above CP and then gives 10% discount.
Take CP = 100.
MP = 125 and SP = 125 × 0.90 = 112.5.
Therefore profit = 12.5%.
Do not simply subtract 10 from 25.
10. Target Profit with Discount
Example: An article costs ₹800. A shopkeeper wants 20% profit after offering 20% discount. Find required MP.
Required SP = 800 × 1.20 = ₹960.
₹960 is 80% of MP.
MP = 960 × 100/80 = ₹1,200.
11. Same Selling Price, Profit on One and Loss on Another
Suppose two articles are sold at the same SP of ₹1,200. One is sold at 20% profit and the other at 20% loss.
First CP = 1,200 × 100/120 = ₹1,000.
Second CP = 1,200 × 100/80 = ₹1,500.
Total CP = ₹2,500 and total SP = ₹2,400.
Net loss = ₹100, so loss% = 100/2,500 × 100 = 4%.
Equal profit and loss percentages do not cancel when the cost bases differ.
12. Quantity and Unit Language
Some questions hide the real base inside quantity wording such as “per kilogram”, “per item”, “dozen”, “total quantity” or “effective cost”.
Before calculating, decide whether the given value refers to one unit or the complete transaction.
Do not mix unit price with total price.
13. Short-Weight or Effective-Quantity Pattern
In some exam questions, a trader charges for a full unit but delivers less quantity. This changes the effective cost per delivered unit.
For example, if 900 g is given while charging for 1 kg, the customer effectively receives only 90% of the stated quantity.
Such questions should be translated into effective quantity or effective cost before calculating profit.
14. A Four-Step Translation Framework
- Identify: underline CP, SP, MP, discount, profit or loss words.
- Choose the base: CP for profit/loss, MP for discount unless stated otherwise.
- Write the relation: convert the sentence into a multiplier, ratio or formula.
- Calculate and check: verify that the final direction makes sense.
For formula revision, see Profit and Loss Formulas for Exams.
15. Common Word-Problem Traps
- Starting arithmetic too early: translate the words first.
- Mixing MP and CP: discount and profit may use different bases.
- Reversing percentages incorrectly: final value must first be identified as a percentage of the original.
- Ignoring quantity: total price and unit price are not interchangeable.
- Assuming same percentage means same amount: percentage amounts depend on the base.
- Forcing a shortcut: use a shortcut only when its condition matches.
For dedicated error diagnosis, use Common Profit and Loss Mistakes.
16. Solved Word Problems
Example 1: A trader buys a bag for ₹640 and sells it for ₹800. Profit = ₹160, so profit% = 25%.
Example 2: An item marked ₹2,000 is sold at 15% discount. SP = ₹1,700.
Example 3: An article is sold for ₹1,080 at 10% discount. MP = 1,080 × 100/90 = ₹1,200.
Example 4: An item is sold for ₹540 at 10% loss. CP = 540 × 100/90 = ₹600.
17. Quick Practice Check
- A trader buys an article for ₹500 and sells it for ₹625. Find profit%.
- An article costing ₹900 is sold at 20% loss. Find SP.
- A watch marked ₹1,500 is sold at 12% discount. Find SP.
- An article is sold for ₹960 at 20% profit. Find CP.
- MP is ₹2,400 and SP is ₹2,040. Find discount%.
- An article costs ₹1,000, is marked 25% above CP and sold at 10% discount. Find profit%.
Answers: (1) 25%; (2) ₹720; (3) ₹1,320; (4) ₹800; (5) 15%; (6) 12.5%.
18. Next Step
For the complete chapter map, return to the Profit and Loss Master Guide. For faster translation and calculation methods, use Profit and Loss Tricks for Faster Solving.
Then apply this translation method in Exam-Based Profit and Loss Questions and Profit and Loss Practice Set 1.