Percentage Practice Test 1 with solutions

Let the number of books owned by B = x
Number of books owned by A = $\frac{4}{5}\mathit{x}$
25% of books of A is transfered to B.
Firstly, $\frac{4}{5}\mathit{x}\times \frac{25}{100}=\frac{\mathit{x}}{5}$ books transfer to B
⇒ Books owned by B = $\mathit{x}+\frac{\mathit{x}}{5}=\frac{6}{5}\mathit{x}$
Books owned by A = $\frac{4}{5}\mathit{x}-\frac{\mathit{x}}{5}=\frac{3}{5}\mathit{x}$
Now 25% of books of B is transfered to A.
So, $\frac{6}{5}\mathit{x}\times \frac{25}{100}=\frac{3}{10}\mathit{x}$
Books owned by B $=\frac{6}{5}\mathit{x}-\frac{3}{10}\mathit{x}=\frac{9}{10}\mathit{x}$
Books owned by A $=\frac{3}{5}\mathit{x}+\frac{3}{10}\mathit{x}=\frac{9}{10}\mathit{x}$
Percentage of the total number of books that A has $=\frac{\mathrm{Books}\mathrm{of}\mathit{A}}{\mathrm{Total}\mathrm{books}}\times 100$
$=\frac{\frac{9}{10}\mathit{x}}{\frac{9}{10}\mathit{x}+\frac{9}{10}\mathit{x}}\times 100=50$
∴ A has 50% of total number of books.