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 ?
A. Rs. 1890
B. Rs. 2100
C. Rs. 2200
D. Rs. 2457
E. None of these
Answer: Option D
Solution(By Examveda Team)
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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A. $$\frac{1}{4}$$
B. $$\frac{1}{3}$$
C. $$\frac{1}{2}$$
D. $$\frac{2}{3}$$
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