ABC26GN5808 · Line Graphs

Let the incomes of X and Y in 2010 be ₹ $3 x$ and ₹ $4 x$ respectively and let their expenditures be $E_{1}$ and $E_{2}$ respectively. Then, $\frac{\left(3 x-E_{1}\right)}{E_{1}} \times 100=65$ and $\frac{\left(4 x-E_{2}\right)}{E_{2}} \times 100=50$ $$\begin{aligned} & \Rightarrow \quad \frac{3 x}{E_{1}}-1=\frac{65}{100} \text { and } \frac{4 x}{E_{2}}-1=\frac{50}{100} \\ & \Rightarrow \quad \frac{3 x}{E_{1}}=\left(\frac{13}{20}+1\right) \text { and } \frac{4 x}{E_{2}}=\left(\frac{1}{2}+1\right) \\ & \Rightarrow \quad \frac{3 x}{E_{1}}=\frac{33}{20} \text { and } \frac{4 x}{E_{2}}=\frac{3}{2} \\ & \Rightarrow \quad E_{1}=\frac{60 x}{33}=\frac{20 x}{11} \text { and } E_{2}=\frac{8 x}{3} \\ & \Rightarrow E_{1}: E_{2}=\frac{20 x}{11}: \frac{8 x}{3}=60: 88=15: 22 \end{aligned}$$