The marked price of an article is ₹ 625. After allowing a discount of 32% on the marked price, there was a profit of ₹25. The profit percentage (correct to the nearest integer) is:

To find the profit percentage, we need to first calculate the selling price (SP) and then the cost price (CP) of the article.

Step 1: Calculate the Selling Price (SP)
The marked price (MP) of the article is ₹ 625.
A discount of 32% is allowed on the marked price.
Discount Amount = 32% of MP
Discount Amount = $\frac{32}{100}\times 625$
Discount Amount = $0.32\times 625=200$
Therefore, the Selling Price (SP) is:
SP = Marked Price - Discount Amount
SP = $625-200=425$
So, the Selling Price is ₹ 425.

Step 2: Calculate the Cost Price (CP)
We are given that the profit made on the sale is ₹ 25.
Profit = Selling Price (SP) - Cost Price (CP)
CP = Selling Price (SP) - Profit
CP = $425-25=400$
So, the Cost Price of the article is ₹ 400.

Step 3: Calculate the Profit Percentage
The formula for profit percentage is:
Profit Percentage = $\frac{\text{Profit}}{\text{Cost Price (CP)}}\times 100$
Profit Percentage = $\frac{25}{400}\times 100$
Profit Percentage = $\frac{25}{4}=6.25\%$

Rounding 6.25% to the nearest integer gives 6%.

Thus, the profit percentage correct to the nearest integer is 6%.