Percent change

If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?

Correct result:

p =  12.5 %

Solution:

q1=1+25/100=54=1.25 q2=110/100=910=0.9  S1=ab S2=(a q1) (b q2)  p=100 S2S1S1  p=100 (a q1) (b q2)abab  p=100 q1 q211=100 1.25 0.911=252=12.5%q_{1}=1+25/100=\dfrac{ 5 }{ 4 }=1.25 \ \\ q_{2}=1-10/100=\dfrac{ 9 }{ 10 }=0.9 \ \\ \ \\ S_{1}=ab \ \\ S_{2}=(a \cdot \ q_{1}) \cdot \ (b \cdot \ q_{2}) \ \\ \ \\ p=100 \cdot \ \dfrac{ S_{2}-S_{1} }{ S_{1} } \ \\ \ \\ p=100 \cdot \ \dfrac{ (a \cdot \ q_{1}) \cdot \ (b \cdot \ q_{2}) - ab }{ ab } \ \\ \ \\ p=100 \cdot \ \dfrac{ q_{1} \cdot \ q_{2}-1 }{ 1 }=100 \cdot \ \dfrac{ 1.25 \cdot \ 0.9-1 }{ 1 }=\dfrac{ 25 }{ 2 }=12.5 \%



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