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The sum of two numbers is 2490. If 6.5 % of one number is equal to 8.5 % of the other then the numbers are:_________?

Correct answer: D. 1411, 1079

  • A. 989, 1501
  • B. 1011, 1479
  • C. 1401, 1089
  • D. 1411, 1079

Explanation

Let the numbers be x and y. Since 6.5% of x equals 8.5% of y, 6.5x = 8.5y, so x:y = 8.5:6.5 = 17:13; their total of 2490 gives 30 parts = 2490, hence x = 17 × 83 = 1411 and y = 13 × 83 = 1079. A student may choose c, 1401 and 1089, because those numbers have the correct total but do not satisfy the percentage relation.

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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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