Multiple choice

After two successive increases, the rent of an apartment became 209.44% of its original amount. If the percentage increase in second increment was 1.5 times the first, what was the percentage increase in the first hike?

  1. 32

  2. 34

  3. 36

  4. 40

  5. a
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the first increase be x%. The second increase is 1.5x%. The final amount is 209.44% of the original, meaning (1 + x/100) * (1 + 1.5x/100) = 2.0944. Solving the quadratic equation x^2 + 166.67x - 7333.33 = 0 gives x = 36.

AI explanation

Using the successive percentage increase formula, the final rent is 209.44% of the original, meaning the total growth multiplier is 2.0944. Let the first percentage increase be r%, so the second is 1.5r%, giving the equation (1 + r/100) multiplied by (1 + 1.5r/100) equals 2.0944. Solving this quadratic equation gives r = 36. The percentage increase in the first hike was 36.

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