Two numbers, x and y are in the ratio 4 : 9 respectively. When 6 is a numbers, the ratio becomes 7 : 12. If 7 is added to each of the origi new ratio.

Let the two numbers be $x$ and $y$.
Given that their ratio is $4:9$, we can write:

$$\frac{x}{y} = \frac{4}{9}$$

So, we can express $x$ and $y$ as $x = 4k$ and $y = 9k$ for some constant $k$.

When 6 is added to each number, the ratio becomes $7:12$.

$$\frac{x+6}{y+6} = \frac{7}{12}$$

Substitute $x=4k$ and $y=9k$ into this equation:

$$\frac{4k+6}{9k+6} = \frac{7}{12}$$

Cross-multiply to solve for $k$:

$$12(4k+6) = 7(9k+6)$$ $$48k + 72 = 63k + 42$$

Subtract $48k$ from both sides:

$$72 = 15k + 42$$

Subtract 42 from both sides:

$$30 = 15k$$

Divide by 15:

$$k = \frac{30}{15}$$ $$k = 2$$

Using $k=2$:

$$x = 4k = 4(2) = 8$$ $$y = 9k = 9(2) = 18$$

The original numbers are 8 and 18.

New $x' = x+7 = 8+7 = 15$
New $y' = y+7 = 18+7 = 25$
The new ratio is $\frac{x'}{y'} = \frac{15}{25}$.
Simplify the ratio by dividing both numbers by their greatest common divisor, which is 5:

$$\frac{15 \div 5}{25 \div 5} = \frac{3}{5}$$

The new ratio is $3:5$.