Given:
The ratio of profit to discount on an item is 4:5.
The marked price of the item is Rs 45 more than the cost price.

To Find:
The discount percent given on the marked price of the item.

Assumptions:
Let the cost price of the item be 'C'.
Let the profit on the item be 'P'.
Let the discount on the item be 'D'.
Let the marked price of the item be 'M'.

Solution:

Step 1: Calculate the cost price (C)
Given that the marked price (M) is Rs 45 more than the cost price (C), we can write the equation M = C + 45. Rearranging the equation, we get C = M - 45.

Step 2: Calculate the profit (P)
The ratio of profit to discount is given as 4:5. Let the common ratio be 'x'. So, we can write the equation P/D = 4/5. Rearranging the equation, we get P = (4/5) * D.

Step 3: Calculate the selling price (S)
The selling price (S) can be calculated by adding the cost price (C) and the profit (P). So, we have S = C + P.

Step 4: Calculate the discount (D)
The discount (D) can be calculated by subtracting the selling price (S) from the marked price (M). So, we have D = M - S.

Step 5: Calculate the discount percent
The discount percent can be calculated by dividing the discount (D) by the marked price (M) and multiplying by 100. So, the discount percent is given by (D/M) * 100.

Step 6: Substitute the values and calculate the discount percent
Substituting the values of C, P, and D from the previous steps, we can calculate the discount percent.

Step 7: Simplify the expression to find the discount percent
By simplifying the expression, we can find the discount percent.

Step 8: Final Answer
The discount percent given on the marked price of the item is the result obtained in Step 7.

Conclusion:
The discount percent given on the marked price of the item is calculated by dividing the discount by the marked price and multiplying by 100. The discount percent can be found by substituting the values of cost price, profit, and discount in the given equation and simplifying it.