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?

Correct result:

a =  25 %
b =  30 h
c =  12.5 %

Solution:

p=300 Kc/h v=p+p/3=300+300/3=400 Kc/h  h2=60 h h2=h1h1/3 h1=h2/(113)=60/(113)=90 h  a=100 vpv=100 400300400=25%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 \%
b=h1h2=9060=30 hb=h_{1}-h_{2}=90-60=30 \ \text{h}
z1=p h1=300 90=27000 Kc z2=v h2=400 60=24000 Kc  c=100 z1z2z2=100 270002400024000=252=12.5%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 \%



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