A doll 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:

Correct Answer: The rate of the second discount is 20%.

Let's break down the solution step-by-step to understand how the final price is calculated after two successive discounts.

Step 1: Understand the given values
Marked Price (MP) of the doll = ₹2,500
Final Selling Price (SP) paid by the customer = ₹1,800
Rate of the first discount (d₁) = 10%

Step 2: Calculate the price after the first discount
The first discount is 10% on the Marked Price of ₹2,500.

$\text{First Discount Amount}=10\%\text{of}2500=\frac{10}{100}\times 2500=250$

Price after the first discount = Marked Price - First Discount Amount

$\text{Price after 1st discount}=2500-250=2250$

So, after the first discount, the reduced price of the doll is ₹2,250.

Step 3: Calculate the second discount amount
The customer actually pays ₹1,800. The remaining reduction in price is due to the second discount.

$\text{Second Discount Amount}=2250-1800=450$

Step 4: Calculate the rate of the second discount
The second discount is applied to the price after the first discount (₹2,250).

$\text{Rate of 2nd Discount}=\left(\frac{\text{Second Discount Amount}}{\text{Price after 1st Discount}}\right)\times 100$

$\text{Rate of 2nd Discount}=\left(\frac{450}{2250}\right)\times 100=\frac{1}{5}\times 100=20\%$

Thus, the rate of the second discount is 20%.