Let the cost price of the product be \(x\).
In the case of a 19% loss, the selling price is:
\(\Rightarrow\;\)\(\text{SP}_1 = x - 0.19x = 0.81x\)
In the case of a 17% profit, the selling price is:
\(\Rightarrow\;\)\(\text{SP}_2 = x + 0.17x = 1.17x\)
The increase in selling price is given as Rs 162:
\(\Rightarrow\;\)\(\text{SP}_2 - \text{SP}_1 = 162\)
\(\Rightarrow\;\)\(1.17x - 0.81x = 162\)
\(\Rightarrow\;\)\(0.36x = 162\)
\(\Rightarrow\;\)\(x = \frac{162}{0.36} = 450\)
Thus, the cost price of the product is Rs 450.