Difference between revisions of "2007 Cyprus MO/Lyceum/Problem 24"

m (sol)
 
(See also)
Line 8: Line 8:
  
 
==See also==
 
==See also==
{{CYMO box|year=2007|l=Lyceum|num-b=3|num-a=5}}
+
{{CYMO box|year=2007|l=Lyceum|num-b=23|num-a=25}}
  
 
[[Category:Introductory Algebra Problems]]
 
[[Category:Introductory Algebra Problems]]

Revision as of 23:27, 18 January 2024

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 $2(198) - 400 = -4 \Longrightarrow \mathrm{E}$.

See also

2007 Cyprus MO, Lyceum (Problems)
Preceded by
Problem 23
Followed by
Problem 25
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30