A jacket is marked for $₹2,500$. A customer pays $₹1,800$ for it. If the customer got a series of two discounts and the rate of the first discount is $10\%$, then the rate of the second discount is:

Step 1: Calculate the price after the first discount
Marked Price ($\text{MP}$) of the jacket = $₹2,500$
First discount = $10\%$
Price after the first discount = $2500\times \left(1-\frac{10}{100}\right)=2500\times 0.90=₹2,250$

Step 2: Calculate the second discount percentage
Final price paid by the customer = $₹1,800$
Amount of the second discount = $2250-1800=₹450$
Rate of the second discount = $\left(\frac{450}{2250}\times 100\right)\%=\left(\frac{1}{5}\times 100\right)\%=20\%$

Therefore, the rate of the second discount is $20\%$.