Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week.

Correct result:

p =  14.6 %

Solution:

$r=5+52 \cdot \ 19=993 \ \\ q=\dfrac{ 100 }{ 100-15 }=\dfrac{ 20 }{ 17 } \doteq 1.1765 \ \\ \ \\ b=52 \cdot \ 19 \cdot \ q=52 \cdot \ 19 \cdot \ 1.1765 \doteq \dfrac{ 19760 }{ 17 } \doteq 1162.3529 \ \\ \ \\ p=100 \cdot \ \dfrac{ b-r }{ b }=100 \cdot \ \dfrac{ 1162.3529-993 }{ 1162.3529 }=14.6 \%$

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