Aman's expense is 30% more than Vimal's and Vimal's expense is 10% less than Raman's. If the sum of their expenses is Rs. 6447, then what would be Aman's expense ?

Answer: Option D

Let Raman's expense be Rs. $$x$$
Then, Vimal's expenses :
= 90% of $$x$$
$$\begin{array}{rl}& =\text{ Rs}\text{. }\left(\frac{90}{100}\times x\right)\\ & =\text{Rs}\text{. }\frac{9}{10}x\end{array}$$
Aman's expense :
\begin{aligned} & = {\text{130% of Rs}}{\text{. }}\left( {\frac{{9x}}{{10}}} \right) \\ & = {\text{ Rs}}{\text{. }}\left( {\frac{{130}}{{100}} \times \frac{{9x}}{{10}}} \right) \\ & = {\text{ Rs}}{\text{. }}\frac{{117x}}{{100}} \\ & \therefore \frac{{117x}}{{100}} + \frac{{9x}}{{10}} + x = 6447 \\ & \Rightarrow \frac{{117x + 90x + 100x}}{{100}} = 6447 \\ & \Rightarrow 307x = 644700 \\ & \Rightarrow x = \frac{{644700}}{{307}} \\ & \Rightarrow x = 2100 \\ & {\text{Hence, Aman's expenses :}} \\ & = {\text{Rs}}{\text{. }}\left( {\frac{{117 \times 2100}}{{100}}} \right) \\ & = {\text{Rs}}{\text{. 2457}} \\\end{aligned}