Aman's expense is 30% more than Vimal's and Vimal's expense is 10% less than Raman's. If the sum of their… · ABC26GN2281

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