###### Quantitative Aptitude Quest

** Percentage**

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John started work 2 years ago. Her starting salary was 1/2 of Mike's salary at that time. Each year since then Joan has received a raise of5% in her salary and Mike has received a raise of 10% in his salary. What percentage (to the nearest percent) of Mike's current salary is Joan's current salary? 1. 45 2. 46 3. 48 4. 50
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Let JS and JC be Joan's starting and current salaries respectively. Let Ms and MC be Mike's salary when Joan started and his current salary. We know JS = .5Ms, and we want to find an equation relating JC and Mc. Since Joan received a 5% raise each year, after 1 year her is (1.05)(1.05)JS. In the same way, we can see that Mike's current salary (MC) is = (1.10)(1.10)MS. So Mc = (1.1) Ms. So JC = (1.05)(1.05)Js = 1.1025JS = .5(1.1025)MS = (.55125) (1/(1.1) )MC = (.55125/1.21)MC. Since we want the answer to the nearest percent, we must divide to three decimal places. So, .55125/1.21 = .455 = 46% to the nearest percent.