Let marked price be x
After 12.5 % vat the shoes price will be
x + \(\frac{12.5}{100}x = x \left(1 + \frac{125}{1000}\right)\) \(= (1 + \frac{1}{8})x\) = 9/8 x
There was 20 % discount on any variety of shoes.
\(\therefore\) The paid price will be
\(\frac{9}{8}x - \frac{20}{100} \times \frac{9}{8}x\) \(=(\frac{9}{8}) x (1 - \frac{20}{100})\)
\(=\frac{9}{8}x (1 - \frac{1}{5}) = \frac{9}{8}x \times \frac{4}{5} = \frac{9}{10}x\)
But the paid price is 6752.
\(\therefore\) \(\frac{9}{10}x = 6752\)
\(\Rightarrow\) x \(=6752 \times \frac{10}{9}=7502.22\)
Hence, the marked price of the shoes is Rs 7502.22.