Please solve question 40

The mean of the numbers a, b, 8, 5, 10 is 6 and the variance is 6.80.
Now, using the deifnition of mean we have,
(a + b + 8 + 5 + 10)/ 5 = 6.
This gives a + b = 7. … (1)
Using the definition of variance, we get

$$\begin{gathered} \mathrm{putting} \mathrm{value} \mathrm{of} \mathrm{a} \mathrm{from} \mathrm{equation} 1 \\ {\left(\mathrm{b}-1\right)}^2+{\left(6-\mathrm{b}\right)}^2= 13 \\ 2{\mathrm{b}}^2+37-2\mathrm{b}-12\mathrm{b}= 13 \\ 2{\mathrm{b}}^2-14\mathrm{b}+24=0 \\ {\mathrm{b}}^2-7\mathrm{b}+12=0 \\ {\mathrm{b}}^2-4\mathrm{b}-3\mathrm{b}+12=0 \\ \mathrm{b}\left(\mathrm{b}-4\right)-3\left(\mathrm{b}-4\right)= 0 \\ \left(\mathrm{b}-3\right)\left(\mathrm{b}-4\right)= 0 \\ \mathrm{b} = 3,4 \\ \mathrm{so} \mathrm{a} = 4,3 \\ \mathrm{so} \mathrm{option} \mathrm{C} \end{gathered}$$