# Unknown number 10

Number first increased by 30%, then by 1/5. What percentage we've increased the original number?

Correct result:

p =  56 %

#### Solution:

$b=a(1 + 30/100) \cdot \ (1 + 1/5)=0 \ \\ \ \\ p=100 \cdot \ \dfrac{ b-a }{ a } \ \\ p=100 \cdot \ \dfrac{ a(1 + 30/100) \cdot \ (1 + 1/5)-a }{ a } \ \\ p=100 \cdot \ \dfrac{ (1 + 30/100) \cdot \ (1 + 1/5)-1 }{ 1 } \ \\ p=100 \cdot \ ((1 + 30/100) \cdot \ (1 + 1/5)-1)=56 \%$

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