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If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before?

Correct answer: B. 33 1/3 %

  • A. 27 2/23 %
  • B. 33 1/3 %
  • C. 30%
  • D. 19%

Explanation

Let the original price and quantity be P rupees and Q ornaments. After a 50% price increase, the price is 1.5P rupees, so the new quantity must be Q / 1.5 = 2Q/3 to keep expenditure unchanged. The reduction is Q - 2Q/3 = Q/3 = 33 1/3%. The likely mistake is choosing 27 2/23% by calculating the change from the increased price incorrectly.

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Percentages express a quantity as parts per hundred and support calculations involving increases, decreases, discounts, commissions, taxes, and successive changes. Questions require distinguishing percentage change from percentage points and identifying the original value when a final value and its percentage change are given.

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