**Given Information:**
- The ratio of two numbers is 40/7 to 5.
- Each number is diminished by 25/2.
- After diminishing, the numbers are in the ratio of 11/3 to 3.

**Step 1: Developing equations using the given information**

Let the two numbers be x and y.

From the given information, we can create the following equations:

1. The ratio of x to y is 40/7 to 5:
x/y = (40/7)/5 = 40/7 * 1/5 = 8/7

2. Each number is diminished by 25/2:
(x - 25/2)/(y - 25/2)

3. After diminishing, the numbers are in the ratio of 11/3 to 3:
(x - 25/2)/(y - 25/2) = (11/3)/3 = 11/3 * 1/3 = 11/9

**Step 2: Solving the equations**

To solve these equations, we can use the method of substitution.

We have the first equation: x/y = 8/7

Rearranging this equation, we get: x = (8/7)y

Substituting this value of x in the second equation, we get:

((8/7)y - 25/2)/(y - 25/2) = 11/9

Cross-multiplying, we get:

9((8/7)y - 25/2) = 11(y - 25/2)

Simplifying, we have:

(72/7)y - 225/2 = (11/1)y - 275/2

Multiplying through by 14 to eliminate the fractions, we get:

(72 * 2)y - 225 * 7 = (11 * 14)y - 275 * 7

Simplifying further, we have:

144y - 1575 = 154y - 1925

Rearranging and combining like terms, we get:

10y = 350

Simplifying, we have:

y = 35

Substituting this value of y in the equation x = (8/7)y, we get:

x = (8/7)(35) = 40

Therefore, the two numbers are 40 and 35.

**Step 3: Verifying the solution**

Now, let's verify if the solution satisfies the given conditions.

1. The ratio of the two numbers is 40/7 to 5:
40/35 = 40/7 * 1/5 = 8/7

2. Each number is diminished by 25/2:
(40 - 25/2)/(35 - 25/2) = 75/2 / 60/2 = 75/60 = 5/4

3. After diminishing, the numbers are in the ratio of 11/3 to 3:
(40 - 25/2)/(35 - 25/2) = (11/3)/3 = 11/9

Therefore, the solution satisfies all the given conditions.

Hence, the two numbers are 40 and 35.

40,35