The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If…

Question

The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?

1. A. p(10⁴ − k²)² = q × 10⁸ (Correct answer)
2. B. p(10⁴ − k²)² = q × 10⁴
3. C. p(10⁴ − k²) = q × 10⁴
4. D. p(10⁴ − k²) = q × 10⁸

Correct Answer

Option A — p(10⁴ − k²)² = q × 10⁸

Detailed Solution & Explanation

The correct answer is p(10⁴ − k²)² = q × 10⁸.

Key Points

• Starting price p: after +k%: p(1+k/100); after −k%: p(1−k²/10000); after +k%: p(1−k²/10000)(1+k/100); after −k%: p((1−k²/10000))² = q. So p×((10000−k²)/10000)² = q → p(10⁴−k²)² = q×10⁸.
• Answer: p(10⁴−k²)² = q×10⁸.