At 12% discount, the selling price of a pen is Rs 13.20. Find its marked price. Also, find the new selling price of the pen, if it is sold at 5% discount.

Answer

To solve the problem step by step, we will first find the marked price of the pen using the information given about the discount and selling price. Then, we will calculate the new selling price when the pen is sold at a different discount rate.

### Step 1: Find the Marked Price

We know that the selling price (SP) after a discount is given by the formula:

\[ SP = MP - \text{Discount} \]

Where:
- SP = Selling Price
- MP = Marked Price
- Discount = (Discount Percentage / 100) × MP

Given:
- Selling Price (SP) = Rs 13.20
- Discount Percentage = 12%

Using the formula for discount, we can express the discount in terms of the marked price:

\[ \text{Discount} = \frac{12}{100} \times MP = 0.12 \times MP \]

Now, substituting this into the selling price formula:

\[ 13.20 = MP - 0.12 \times MP \]

This simplifies to:

\[ 13.20 = MP (1 - 0.12) \]
\[ 13.20 = MP \times 0.88 \]

Now, we can solve for MP:

\[ MP = \frac{13.20}{0.88} \]
\[ MP = 15 \]

### Step 2: Find the New Selling Price at 5% Discount

Now that we have the marked price, we can find the new selling price when the discount is 5%.

Using the same formula for selling price:

\[ SP = MP - \text{Discount} \]

Where the new discount is:

\[ \text{Discount} = \frac{5}{100} \times MP = 0.05 \times MP \]

Substituting the marked price we found:

\[ \text{Discount} = 0.05 \times 15 = 0.75 \]

Now, we can find the new selling price:

\[ SP = MP - \text{Discount} \]
\[ SP = 15 - 0.75 \]
\[ SP = 14.25 \]

### Final Answers:
- Marked Price (MP) = Rs 15
- New Selling Price at 5% discount = Rs 14.25

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