40. 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?

Question

Accepted Answer

The correct answer is option A. Let the original price be p.
1.  Price after first increase of k%: p₁ = p * (1 + k/100) = p * (100+k)/100
2.  Price after first decrease of k%: p₂ = p₁ * (1 - k/100) = p * (100+k)/100 * (100-k)/100
    This simplifies to p * (100² - k²)/100² = p * (10000 - k²)/10000
3.  Price after second increase of k%: p₃ = p₂ * (1 + k/100) = p * [(10000 - k²)/10000] * (100+k)/100
4.  Price after second decrease of k% (which is q): q = p₃ * (1 - k/100) = p * [(10000 - k²)/10000] * (100+k)/100 * (100-k)/100
    q = p * [(10000 - k²)/10000] * [(100² - k²)/100²]
    q = p * [(10000 - k²)/10000] * [(10000 - k²)/10000]
    q = p * [(10000 - k²)/10000]²
    q = p * (10⁴ - k²)² / (10⁴)²
    q = p * (10⁴ - k²)² / 10⁸
Rearranging to match the options:
q × 10⁸ = p × (10⁴ - k²)²
Or p(10⁴ – k²)² = q × 10⁸.
This question tests the understanding of successive percentage changes and algebraic manipulation, a fundamental concept in quantitative aptitude for CSAT.

Q40. 40. 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?

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