Profit and Loss becomes easy when the basic quantities are clear. Before learning discount, marked price, successive changes or shortcut formulas, you should be able to identify Cost Price (CP), Selling Price (SP), profit, loss and the correct percentage base without hesitation.
This lesson builds that foundation for SSC, Banking and Railway arithmetic. The goal is not to memorise many tricks. It is to understand what each value means, why profit and loss percentages normally use CP as the base, and how to solve direct and simple reverse questions accurately.
1. What Is Cost Price (CP)?
Cost Price is the amount paid to obtain an item. In most basic questions, CP is the starting value against which profit or loss is measured.
If a shopkeeper buys a bag for ₹800, then CP = ₹800. Extra expenses may sometimes be added to cost in word problems, but only when the question explicitly includes them.
2. What Is Selling Price (SP)?
Selling Price is the amount received when the item is sold.
- If SP is greater than CP, the transaction gives a profit.
- If SP is less than CP, the transaction gives a loss.
- If SP equals CP, there is neither profit nor loss.
Example: CP = ₹500 and SP = ₹650. Since SP is ₹150 above CP, profit = ₹150.
3. Profit and Loss Amount
- Profit = SP − CP
- Loss = CP − SP
Do not use the profit formula when SP is below CP. First compare CP and SP, then decide whether the difference represents profit or loss.
For the full formula system, continue to Profit and Loss Formulas for Exams.
4. Why Profit% and Loss% Use CP as the Base
Profit or loss describes how much the result changed relative to what was originally invested. That original investment is CP, so ordinary profit% and loss% are calculated on CP.
- Profit% = Profit ÷ CP × 100
- Loss% = Loss ÷ CP × 100
Example: CP = ₹400 and SP = ₹500. Profit = ₹100. Profit% = 100 ÷ 400 × 100 = 25%.
A very common beginner mistake is to divide by SP simply because SP appears at the end of the transaction. In standard profit-loss questions, CP remains the percentage base unless the wording explicitly defines another reference value.
5. Direct Question: Find SP at a Profit
If CP = ₹600 and profit = 20%, then profit amount = 20% of 600 = ₹120. Therefore SP = 600 + 120 = ₹720.
The same question can also be solved by the multiplier method: SP = 600 × 1.20 = ₹720. At the basics stage, understand the addition method first; the multiplier becomes useful for speed later.
6. Direct Question: Find SP at a Loss
If CP = ₹800 and loss = 15%, loss amount = 15% of 800 = ₹120. Therefore SP = 800 − 120 = ₹680.
The multiplier form is SP = 800 × 0.85 = ₹680.
7. Reverse Basic: Find CP from SP
Reverse questions require more care because the given selling price already contains the profit or loss.
If an item is sold for ₹720 at 20% profit, then ₹720 represents 120% of CP. Therefore:
CP = 720 × 100 ÷ 120 = ₹600.
Do not simply subtract 20% of ₹720. The 20% profit was calculated on CP, not on the final SP.
8. Marked Price Is Different from Cost Price
Marked Price (MP) is the displayed or listed price before discount. It is not automatically the same as CP or SP.
Discount connects MP to SP, while profit or loss connects CP to SP. Keeping these relationships separate prevents confusion when you later study Discount and Marked Price Questions.
9. Beginner Mistakes to Avoid
- Using the wrong difference: profit is SP − CP; loss is CP − SP.
- Using SP as the denominator: ordinary profit% and loss% normally use CP.
- Confusing discount with loss: discount is based on MP, while loss is based on CP.
- Reversing percentages directly: a 20% profit cannot be undone by simply taking 20% of SP.
- Starting calculation before identifying the values: first mark CP, SP and the requested quantity.
For a deeper error-repair lesson, use Common Profit and Loss Mistakes.
10. Solved Examples
Example 1: CP = ₹720 and SP = ₹675. Loss = 720 − 675 = ₹45. Loss% = 45 ÷ 720 × 100 = 6.25%.
Example 2: CP = ₹840 and SP = ₹910. Profit = 910 − 840 = ₹70. Profit% = 70 ÷ 840 × 100 = 8⅓%.
Example 3: An item costing ₹1,200 is sold at 10% profit. SP = 1,200 × 1.10 = ₹1,320.
11. Quick Practice Check
- CP = ₹500, SP = ₹575. Find profit and profit%.
- CP = ₹900, SP = ₹810. Find loss and loss%.
- An item costs ₹640 and is sold at 25% profit. Find SP.
- An item is sold for ₹540 at 10% loss. Find CP.
- State the correct base for ordinary profit% and loss%.
Answers: (1) ₹75 and 15%; (2) ₹90 and 10%; (3) ₹800; (4) ₹600; (5) CP.
12. What to Learn Next
Once CP, SP, profit, loss and percentage base are clear, return to the Profit and Loss Master Guide for the complete chapter map.
Then move to Profit and Loss Formulas for Exams for formula consolidation, Profit and Loss Tricks for Faster Solving for speed methods, and Profit and Loss Practice Set 1 when you are ready for mixed practice.