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Introduction
In profit and loss questions, you are often given the Cost Price (CP), Selling Price (SP), or the percentage of profit/loss, and asked to find the missing value.
Mastering these relations is crucial for solving problems quickly and accurately.
Pattern: Finding CP or SP
The key idea is to use the relation between CP, SP, and Profit/Loss %.
Profit %: SP = CP × (1 + Profit%/100)
Loss %: SP = CP × (1 - Loss%/100)
Finding CP from SP: CP = SP ÷ (1 ± Profit/Loss%/100)
Step-by-Step Example
Question
A shopkeeper sells an item for ₹600 at a profit of 20%. Find its cost price.
Options:
- A. ₹480
- B. ₹520
- C. ₹500
- D. ₹550
Solution
-
Step 1: Write the relation between SP and CP.
Formula → SP = CP × (1 + Profit%/100). -
Step 2: Substitute given values and simplify.
Substitute values → 600 = CP × 1.2. -
Step 3: Solve for CP.
CP = 600 ÷ 1.2 = ₹500. -
Final Answer:
₹500 → Option C -
Quick Check:
20% of 500 = 100 → SP = 500 + 100 = 600 ✅
Quick Variations
1. If CP and profit % are given → Find SP.
2. If SP and profit % are given → Find CP.
3. If SP and loss % are given → Find CP.
4. If CP and loss % are given → Find SP.
Trick to Always Use
- Step 1: Remember SP = CP × (1 ± %/100).
- Step 2: Rearrange when CP needs to be found.
- Step 3: Always apply + for profit and - for loss.
- Step 4: Quick verify with mental calculation.
Summary
- Use SP = CP × (1 + profit%/100) to get SP when profit% is given.
- Use SP = CP × (1 - loss%/100) to get SP when loss% is given.
- To find CP from SP, divide SP by (1 ± %/100) depending on profit/loss.
- Always perform a quick check: compute % of CP and add/subtract to verify SP.
Example to remember:
If SP = ₹600 at 20% profit → CP = ₹600 ÷ 1.2 = ₹500