Aarav owns a watch worth ₹ $10,000$. He sells it to Bhavin at a profit of $15\%$. After some days, Bhavin sells it back to Aarav at a $15\%$ loss. Find the percentage profit or loss faced by Aarav over the entire transaction.

Let's track the money flow step-by-step for Aarav:
1. Initial state: Aarav has a watch worth ₹ $10,000$.
2. First Sale (Aarav to Bhavin):
Aarav sells it at a $15\%$ profit.

$${\text{Selling Price (SP)}}_1=10000\times \left(1+\frac{15}{100}\right)=\text{₹ }11,500$$

*Aarav now has ₹ $11,500$ in cash, and Bhavin possesses the watch.*
3. Second Sale (Bhavin back to Aarav):
Bhavin sells it back to Aarav at a $15\%$ loss on his cost price (₹ $11,500$).

$${\text{Selling Price (SP)}}_2=11500\times \left(1-\frac{15}{100}\right)=11500\times 0.85=\text{₹ }9,775$$

*Aarav buys it back by paying ₹ $9,775$.*
4. Net calculation for Aarav:
Aarav now has his original watch back (worth ₹ $10,000$) plus some remaining net cash from the transactions:

$$\text{Net Cash Gained}=\text{Cash received}-\text{Cash paid}=11500-9775=\text{₹ }1,725$$

Since Aarav has his original asset back and an additional ₹ $1,725$ in cash, his net gain is ₹ $1,725$.

$$\text{Profit Percentage}=\left(\frac{1725}{10000}\times 100\right)\%=17.25\%\text{ profit}$$