Multiple choice

The salary of A increases by 50% every year, whereas the salary of B increases by 25% every year. If in 2008, their salaries are equal, what percentage of Bs salary was As salary in 2005?

  1. 75%

  2. 58%

  3. 50%

  4. 25%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let A(t) and B(t) be the salaries in year t. Given A(2008) = B(2008), we have A(2005)(1.5)^3 = B(2005)(1.25)^3. The ratio A(2005)/B(2005) = (1.25/1.5)^3 = (5/6)^3 = 125/216, which is approximately 0.5787 or 58%.

AI explanation

Let the common salary in 2008 be S. A's salary in 2005 was S divided by (1.5 cubed), which equals S divided by 3.375, or approximately 0.296S. B's salary in 2005 was S divided by (1.25 cubed), which equals S divided by 1.953125, or approximately 0.512S. A's salary as a percentage of B's salary is (0.296S / 0.512S) multiplied by 100, which is approximately 57.8 percent, which rounds to 58%. The result is 58%.

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