2000 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

Karl had his salary reduced by $10\%$ . He was later promoted and his salary was increased by $10\%$ . If his initial salary was $$20~000$ , what is his present salary?

$\text{ (A) }\ $16~200 \qquad\text{ (B) }\ $19~800 \qquad\text{ (C) }\ $20~000 \qquad\text{ (D) }\ $20~500 \qquad\text{ (E) }\ $24~000$

Solution 1

If Karl's salary was reduced by $10\%$ , that means that $90\%$ of the initial salary was remaining before the promotion. Thus, he had $90\% \times $20~000 = \frac{9}{10} \times $20~000 = $18~000$ left.

After his promotion, this was then raised by $10\%$ , so his salary is $110\%$ times what it was before he got promoted.

$$18 000 \times 110\% = $18~000 \times \frac{11}{10} = \boxed {\textbf {(B) } $19~800}$

~anabel.disher

Solution 2

Let $x$ be the initial salary. After it was reduced, he had $\frac{9}{10}x$ for his salary.

After his promotion, he then had $\frac{9}{10}x \times \frac{11}{10} = \frac{99}{100}x$ for the salary.

Since we know the initial salary was $$20~000$ , we can plug-in $x = $20~000$ . We then have:

$\frac{99}{100} \times $20~000 = \boxed {\textbf {(B) } $19~800}$

~anabel.disher

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2000 CEMC Gauss (Grade 8) Problems/Problem 10

Problem

Solution 1

Solution 2