If A = 10.4 + 10.04 + 10.004 + .... upto 8 terms, then what is the value of A?

Answer: Option C

$$\begin{array}{rl}& \frac{1}{0.4}+\frac{1}{0.04}+\frac{1}{0.004}+....\text{ upto 8 terms}\\ & =\frac{10}{4}+\frac{100}{4}+\frac{1000}{4}+....\text{ upto 8 terms}\\ & =\frac{1}{4}\left[10+100+1000+....\text{ upto 8 terms}\right]\\ & =\frac{1}{4}\left[\frac{10\left({10}^8-1\right)}{10-1}\right]\left(\because S_n=\frac{a\left(r^n-1\right)}{r-1}\right)\\ & =\frac{1}{4\times 9}\times 10\left({10}^4+1\right)\left({10}^4-1\right)\\ & =\frac{10}{4\times 9}\times \left({10}^4+1\right)\left({10}^2+1\right)\left(10+1\right)\left(10-1\right)\\ & =\frac{10}{4\times 9}\times \left({10}^4+1\right)\left({10}^2+1\right)\left(11\right)\left(9\right)\\ & =\frac{10\times 10001\times 101\times 11}{4}\\ & =27777777.5\end{array}$$