2007 Cyprus MO/Lyceum/Problem 24

Problem

Costas sold two televisions for €198 each. From the sale of the first one he made a profit of 10% on its value and from the sale of the second one, he had a loss of 10% on its value. After the sale of the two televisions Costas had in total

$\mathrm{(A) \ } \mathrm{profit\ }4\qquad \mathrm{(B) \ } \mathrm{neither\ profit\ nor\ loss}\qquad \mathrm{(C) \ } \mathrm{loss\ } 8\qquad \mathrm{(D) \ } \mathrm{profit\ }8\qquad \mathrm{(E) \ } \mathrm{loss\ } 4$

Solution

If the TV original prices are $x,\ y$ , then $\frac{11}{10}x = 198$ and $\frac 9{10}y = 198$ ; $x = 180$ and $y = 220$ totaling $400$ ; he loses $2(198) - 400 = -4 \Longrightarrow \mathrm{E}$ .

2007 Cyprus MO, Lyceum (Problems)
Preceded by Problem 3	Followed by Problem 5
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2007 Cyprus MO/Lyceum/Problem 24

Problem

Solution

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