In a medical transaction, 17 times the cost price is equal to 8 times the sum of the cost price and the selling price. What is th…

Question

In a medical transaction, 17 times the cost price is equal to 8 times the sum of the cost price and the selling price. What is the gain or loss percentage?

1. A. Loss 15%
2. B. Gain 17.5%
3. C. Gain 12.5% (Correct answer)
4. D. Loss 30%

Correct Answer

Option C — Gain 12.5%

Detailed Solution & Explanation

The correct answer is Gain 12.5%.

Key Points

• Translate the statement into an equation relating Cost Price (CP) and Selling Price (SP).
• '17 times the cost price = 8 times the sum of CP and SP':
• 17 × CP = 8 × (CP + SP)
• 17 CP = 8 CP + 8 SP → 9 CP = 8 SP → SP/CP = 9/8.
• Since SP > CP, there is a gain.
• Taking CP = 8 units and SP = 9 units:
• Gain % = (SP − CP)/CP × 100 = (1/8) × 100 = 12.5%.
• the profit percentage is always calculated on the cost price, using Gain % = (SP − CP)/CP × 100.
• Reducing the given relation to a simple SP : CP ratio makes the percentage immediate.

Exam Tip

• a ratio SP : CP = 9 : 8 always means a 12.5% gain; SP : CP = 8 : 9 would mean an 11.11% loss — worth memorising these common ratio-to-percentage conversions.