A fruit vendor bought 150 mangoes. He sold them at such a price that the selling price of 120 mangoes equals the cost price of 150 mangoes. Find his profit percentage.

The correct option is 25%.

Step-by-Step Explanation:

Step 1: Understand the Given Information

Let the cost price (CP) of 1 mango be $x$.

Therefore, the cost price of 150 mangoes is:

$\text{CP of 150 mangoes}=150x$

According to the question, the selling price (SP) of 120 mangoes is equal to the cost price of 150 mangoes:

$\text{SP of 120 mangoes}=\text{CP of 150 mangoes}=150x$

Step 2: Find the Selling Price of 1 Mango

From the above relation, the selling price of 1 mango is:

$\text{SP of 1 mango}=\frac{150x}{120}=\frac{5}{4}x=1.25x$

Step 3: Calculate the Profit per Mango

Profit on 1 mango is calculated as:

$\text{Profit}=\text{SP}-\text{CP}$

$\text{Profit}=1.25x-x=0.25x$

Step 4: Calculate the Profit Percentage

The formula for profit percentage is:

$\text{Profit Percentage}=\left(\frac{\text{Profit}}{\text{CP}}\right)\times 100$

Substituting the values:

$\text{Profit Percentage}=\left(\frac{0.25x}{x}\right)\times 100=25\%$

Thus, the vendor made a profit of 25%.