If bananas are bought at the rate of $60$ for ₹50 and sold at the rate of $50$ for ₹60, what is the profit percent?

Let's assume a total number of bananas to avoid fractions. Let total bananas be $\text{LCM}(60,50)=300$.
* Cost Price ($\text{C.P.}$) of $300$ bananas = $\frac{50}{60}\times 300=\text{₹}250$
* Selling Price ($\text{S.P.}$) of $300$ bananas = $\frac{60}{50}\times 300=\text{₹}360$

Profit amount:

$$\text{Profit}=\text{S.P.}-\text{C.P.}=360-250=\text{₹}110$$

Profit percentage:

$$\text{Profit}\%=\frac{\text{Profit}}{\text{C.P.}}\times 100=\frac{110}{250}\times 100=11\times 4=44\%$$