A shopkeeper gained 20% on selling a product.
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A shopkeeper gained 20% on selling a product. If he had bought the product at 20% less, and sold it for Rs 8 more, then he would have gained (200/3)%. What was the cost price of the product?
Show answer & explanation
Set up equations for the two scenarios. In scenario 1, the shopkeeper gains 20% on cost price C, so selling price = 1.2C. In scenario 2, the new cost is 0.8C, new selling price is 1.2C + 8, and gain is 200/3% = 6.67%. Solving the equation 1.2C + 8 = 0.8C × (1 + 200/300) yields C = 80.
Step-by-step Derivation:
Let cost price = C
Scenario 1 (Actual):
- Gain = 20%
- Selling Price (SP₁) = C + 0.20C = 1.2C
Scenario 2 (Hypothetical):
- New Cost Price (CP₂) = C - 0.20C = 0.8C
- New Selling Price (SP₂) = SP₁ + 8 = 1.2C + 8
- Gain % = 200/3 % = 66.67%
Gain formula: Gain% = (SP - CP)/CP × 100
For Scenario 2:
200/3 = [(1.2C + 8) - 0.8C] / 0.8C × 100
200/3 = (0.4C + 8) / 0.8C × 100
200/3 ÷ 100 = (0.4C + 8) / 0.8C
2/3 = (0.4C + 8) / 0.8C
Cross multiply:
2 × 0.8C = 3 × (0.4C + 8)
1.6C = 1.2C + 24
0.4C = 24
C = 60
Wait, let me recalculate:
2/3 × 0.8C = 0.4C + 8
1.6C/3 = 0.4C + 8
1.6C = 1.2C + 24
0.4C = 24
C = 60
Verification with C = 60:
- Scenario 1: SP₁ = 1.2 × 60 = 72
- Scenario 2: CP₂ = 0.8 × 60 = 48, SP₂ = 72 + 8 = 80
- Gain in Scenario 2 = (80 - 48)/48 × 100 = 32/48 × 100 = 66.67% = 200/3% ✓
The cost price is Rs. 60 (Option B).