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UPSC PYQPrelims 2025

Civil Services Examination · Question 10

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. p(10^4 - k^2)^2 = q × 10^8
  2. p(10^4 - k^2)^2 = q × 10^4
  3. p(10^4 - k^2) = q × 10^4
  4. p(10^4 - k^2) = q × 10^8
Show answer & explanation

Answer: (A) p(10^4 - k^2)^2 = q × 10^8

Explanation

q = p(1 + k/100)²(1 - k/100)² = p(10^4 - k²)²/10^8. (Answer as per the official UPSC answer key.)