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 ?

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 ? Correct Answer Rs. 2457

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