Question

A number increased by $20\%$, and the resulting number then decreased by $30\%$. By what overall percentage the original value increase or decrease?

• A. It decreased by $21\%$
• B. It decreased by $16\%$
• C. It decreased by $10\%$
• D. It decreased by $8\%$
• E. It increased by $10\%$

Answer 1

The correct option is B It decreased by $16\%$

Let the original number be $n$
As it is first increased by $20$ $\%$, new number $n_1=(100+20)$ $\%$ of $n=\frac{120}{100}\times n$
Now, since this new number is decreased by $30$ $\%$, the resulting number will be
$n_2=(100-30)$ % of $n_1=\frac{70}{100}\times \frac{120}{100}\times n=\frac{84}{100}n$
This means, $n_2=84$% of $n$.
Hence, the resulting number is the original number decreased by $(100-84)=16$ $\%$ of the original number.