Arvind deposited a sum of money with a bank on 1^st january, 2012 at 8% simple interest per annum. He received an amount 3144 on 7^th August, 2012. The money he deposited with the bank was = ?

$$\eqalign{ & {\text{According to the question,}} \cr & {\text{Amount = Rs}}{\text{. 3144}} \cr & {\text{Rate = 8}}\% \cr & {\text{Let, Principal = Rs}}{\text{. }}x \cr & \therefore {\text{Time = }} \cr & \frac{{30 + 29 + 31 + 30 + 31 + 30 + 31 + 7}}{{366}} \cr & = \frac{{219}}{{366}} \cr & \therefore {\text{SI = }}\frac{{{\text{P}} \times {\text{R}} \times {\text{T}}}}{{100}} \cr & \Rightarrow 3144 - x = \frac{{x \times 8 \times 219}}{{100 \times 366}} \cr & = {\text{Rs}}{\text{. 3000}} \cr & \cr & {\bf{Alternate}} \cr & \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{{219}}{{365}}}}{{100}} = 3144 \cr & \Rightarrow {\text{P}} + \frac{{{\text{P}} \times 8 \times \frac{3}{5}}}{{100}} = 3144 \cr & \Rightarrow 100{\text{P}} + \frac{{24{\text{P}}}}{5} = 314400 \cr & \Rightarrow \frac{{524{\text{P}}}}{5} = 314400 \cr & \Rightarrow {\text{P = }}\frac{{314400 \times 5}}{{524}} \cr & \Rightarrow {\text{P}} = {\text{600}} \times {\text{5}} \cr & \Rightarrow {\text{P = Rs}}{\text{.}} \, 3000 \cr} $$