Calculate Second Consecutive Discount on Mobile Price

This problem involves calculating the second discount percentage when two consecutive discounts are applied to the printed price of a mobile, resulting in a specific selling price.

Here is the information given:

• Printed Price (MRP) of the mobile = Rs. 6,400
• Selling Price of the mobile = Rs. 2,560
• First Discount = 20%
• We need to find the Second Discount percentage.

Step 1: Calculate the price after the first discount

The first discount of 20% is applied to the Printed Price (MRP). The amount of the first discount is:

\(\text{First Discount Amount} = 20\% \text{ of MRP}\)

\(\text{First Discount Amount} = \frac{20}{100} \times 6400\)

\(\text{First Discount Amount} = 0.20 \times 6400\)

\(\text{First Discount Amount} = 1280\)

So, the price after the first discount is:

\(\text{Price after 1st Discount} = \text{MRP} - \text{First Discount Amount}\)

\(\text{Price after 1st Discount} = 6400 - 1280\)

\(\text{Price after 1st Discount} = 5120\)

The price of the mobile after the first 20% discount is Rs. 5,120.

Step 2: Determine the second discount percentage

The second discount is applied to the price after the first discount (Rs. 5,120) to arrive at the final Selling Price (Rs. 2,560).

Let the second discount percentage be \(d\%\). The second discount amount is \(d\%\) of Rs. 5,120.

The formula connecting these values is:

\(\text{Selling Price} = \text{Price after 1st Discount} - \text{Second Discount Amount}\)

\(\text{Selling Price} = \text{Price after 1st Discount} - (d\% \text{ of Price after 1st Discount})\)

We can write this as:

\(2560 = 5120 - \left(\frac{d}{100} \times 5120\right)\)

Rearranging the equation to solve for \(d\):

\(2560 = 5120 \left(1 - \frac{d}{100}\right)\)

Divide both sides by 5120:

\(\frac{2560}{5120} = 1 - \frac{d}{100}\)

\(0.5 = 1 - \frac{d}{100}\)

Now, isolate the term with \(d\):

\(\frac{d}{100} = 1 - 0.5\)

\(\frac{d}{100} = 0.5\)

Multiply both sides by 100 to find \(d\):

\(d = 0.5 \times 100\)

\(d = 50\)

So, the second discount is 50%.

Alternatively, we can directly calculate the total percentage reduction from the original price, but calculating step-by-step for each discount is usually clearer for consecutive discounts.

Summary

The mobile was priced at Rs. 6,400. After the first 20% discount, the price became Rs. 5,120. A second discount was applied to Rs. 5,120, bringing the price down to Rs. 2,560. This means the second discount amount was \(5120 - 2560 = 2560\) Rs. Since the discount amount (Rs. 2560) is exactly half of the price before the second discount (Rs. 5120), the second discount percentage is 50%.

The final answer is 50%.