The marked price of watch was Rs. 820. A man bought the same for Rs. 570.72 after getting two successive discounts of which the first was 20%. The rate of second discount was -

Answer: Option B

Let the second discount rate be x%
Then,
(100 - x)% of 80% of 820 = 570.72
$$\begin{array}{rl}& \Rightarrow \frac{\left(100-x\right)}{100}\times \frac{80}{100}\times 820=570.72\\ & \Rightarrow \left(100-x\right)=\left(\frac{57072}{8\times 82}\right)=87\\ & \Rightarrow x=13\end{array}$$
∴ Second discount rate = 13%