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:

$$\begin{gathered} b=a(1+30\mathrm{/}100)\cdot (1+1\mathrm{/}5)=0 \\ p=100\cdot {\displaystyle \frac{b-a}{a}} \\ p=100\cdot {\displaystyle \frac{a(1+30\mathrm{/}100)\cdot (1+1\mathrm{/}5)-a}{a}} \\ p=100\cdot {\displaystyle \frac{(1+30\mathrm{/}100)\cdot (1+1\mathrm{/}5)-1}{1}} \\ p=100\cdot ((1+30\mathrm{/}100)\cdot (1+1\mathrm{/}5)-1)=56\mathrm{\%} \end{gathered}$$

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