Here we can use the formula

$$\begin{gathered} \text{Average (A)=}\frac{\mathrm{Sum} \mathrm{of} \mathrm{observations} \left(\mathrm{S}\right)}{\mathrm{No}. \mathrm{of} \mathrm{observations} \left(\mathrm{N}\right)} \\ \text{⇒ S=A×N} \end{gathered}$$

According to the question,

Sum of 6 observations (A=12, N=6)

⇒S=12 X 6 =72

Later, Average decreased by 1 and number of observations increased by 1 (so A=11, N=7)

So, sum of 7 observations

⇒S=11 X 7 =77

Now,

7th observation=(sum of 7 observations)-(Sum of 6 observations)

therefore, 7th observation=77-72=5

Hence, Option C is correct.