The mean of 13 observations is 35. Three more observations with the same values are included, and the new mean becomes 32. Find the value of the new observations.

Given that the initial mean of 13 observations is 35.

As, 

$\boxed{\mathbf{Mean}\mathbf{ }\mathbf{=}\mathbf{ }\frac{\mathbf{Sum}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{all}\mathbf{ }\mathbf{observations}}{\mathbf{Number}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{observations}}}$

→ $35 = \frac{\mathrm{Sum} \mathrm{of} \mathrm{Initial} \mathrm{Observations}}{13}$

→ Sum of initial observations = 13 $\times$ 35 

→ Sum of initial observations = 455

Now, three more observations with the same values are included, and the new mean becomes 32.

Let the value of each new observation be x.

After adding 3 new observations, the total number of observations becomes: 13 + 3 = 16

Then, 

The new sum of all 16 observations = 16 $\times$ 32 = 512

Now, 

To find the sum of the 3 new observations, subtract the sum of the initial 13 observations from the sum of all 16 observations:

→ 512 - 455 = 57

So, the sum of the three new observations is 57. 

Since there are 3 new observations with the same value are added.

Then, the value of each new observation = $\frac{57}{3}$ = 19 

Therefore, the value of each new observation is 19.