Correct Answer: (1)

Solution: (1) In 2013, income of company $A=Rs$. $I_{1}$ lakhs and its expenditure $=$ Rs. $E_{1}$ lakhs Income of company $B=$ Rs. $I_{2}$ lakhs and its expenditure $=$ Rs. $E_{1}$ lakhs

$\therefore \frac{I_{1}-E_{1}}{E_{1}}=\frac{40}{100}=\frac{2}{5}$

$\Rightarrow 5 I_{1}-5 E_{1}=2 E_{1}$

$\Rightarrow 5 I_{1}=7 E$

Again,

$\frac{I_{2}-E_{1}}{E_{1}}=\frac{45}{100}=\frac{9}{20}$

$\Rightarrow 2 I_{2}-20 E_{1}=9 E_{1}$

$\Rightarrow 20 I_{2}=29 E$

By equation (i) $\times 4+$ (ii),

$20\left(I_{1}+I_{2}\right)=28 E_{1}+29 E_{1}$ $\Rightarrow 20 \times 5.7=57 E_{1}$

$\Rightarrow E_{1}=\frac{20 \times 5.7}{57}=$ Rs. 2 lakhs

$\therefore$ Total expenditure

$=$ Rs. 4 lakhs