# Paul earned

Paul earned 300 Kč in one hour, Václav 1/3 more than Paul. Václav worked 60 hours, which is 1/3 fewer hours than Paul worked.
How many percents less earned Paul an hour than Václav?

How many hours did Paul more than Václav?

How much did Paul earn more than Václav?

Result

a =  25 %
b =  30 h
c =  12.5 %

#### Solution:

$p=300 \ \text{Kc/h} \ \\ v=p + p/3=300 + 300/3=400 \ \text{Kc/h} \ \\ \ \\ h_{ 2 }=60 \ \text{h} \ \\ h_{ 2 }=h_{ 1 }-h_{ 1 }/3 \ \\ h_{ 1 }=h_{ 2 }/(1-\dfrac{ 1 }{ 3 } )=60/(1-\dfrac{ 1 }{ 3 } )=90 \ \text{h} \ \\ \ \\ a=100 \cdot \ \dfrac{ v-p }{ v }=100 \cdot \ \dfrac{ 400-300 }{ 400 }=25=25 \\%$
$b=h_{ 1 }-h_{ 2 }=90-60=30 \ \text{h}$
$z_{ 1 }=p \cdot \ h_{ 1 }=300 \cdot \ 90=27000 \ \text{Kc} \ \\ z_{ 2 }=v \cdot \ h_{ 2 }=400 \cdot \ 60=24000 \ \text{Kc} \ \\ \ \\ c=100 \cdot \ \dfrac{ z_{ 1 }-z_{ 2 } }{ z_{ 2 } }=100 \cdot \ \dfrac{ 27000-24000 }{ 24000 }=\dfrac{ 25 }{ 2 }=12.5=12.5 \\%$

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