on selling a bat at 5/7th of its marked price, the store earns 15% profit. what is the profit earned if it is sold at marked price?

Let the marked price (MP) of the bat be 7x. Given:
It is sold at 57\frac{5}{7}75​ of its marked price and the store earns 15% profit. So,
Selling price at first = 57×7x=5x\frac{5}{7}\times 7x=5x75​×7x=5x Let cost price (CP) = C. Then,

\text{Profit}=15%\Rightarrow 5x=1.15C \RightarrowC=\frac{5x}{1.15}

Now, if the bat is sold at marked price, then
New selling price = MP = 7x. Profit percentage at MP:

\text{Profit}=7x-C=7x-\frac{5x}{1.15}

\text{Profit %}=\frac{7x-\frac{5x}{1.15}}{\frac{5x}{1.15}}\times 100 =\left(\frac{7\times 1.15-5}{5}\right)\times 100 =\left(\frac{8.05-5}{5}\right)\times 100 =\frac{3.05}{5}\times 100 =61%

So, the profit earned if it is sold at the marked price is 61%.

Mini breakdown (story-style)

Think of the bat’s marked price as 7 “money units.”
When the shop sells it at only 5 of those 7 units, it still makes a 15% profit.
That means the cost must be even lower than 5 units. When you then sell it at the full 7 units, the gap between cost and selling price becomes much bigger — and that gap turns into a 61% profit instead of just 15%.

Key formulas used

• Profit % = \frac{\text{SP}-\text{CP}}{\text{CP}}\times 100
• Here, first SP = \frac{5}{7}\times \text{MP}, second SP = MP.

HTML table (as requested)

html

<table>
  <tr>
    <th>Term</th>
    <th>Value (in x)</th>
  </tr>
  <tr>
    <td>Marked Price (MP)</td>
    <td>7x</td>
  </tr>
  <tr>
    <td>Selling Price at 5/7 MP</td>
    <td>5x</td>
  </tr>
  <tr>
    <td>Given Profit at 5/7 MP</td>
    <td>15%</td>
  </tr>
  <tr>
    <td>Cost Price (CP)</td>
    <td>5x / 1.15</td>
  </tr>
  <tr>
    <td>Selling Price at MP</td>
    <td>7x</td>
  </tr>
  <tr>
    <td>Profit % at MP</td>
    <td>61%</td>
  </tr>
</table>

TL;DR:
If the bat is sold at its full marked price, the store earns a 61% profit.