Let the revenue of company $Q$ in $2014$ be $₹ x.$
Then the revenue of company $Q$ in $2015 = x + x \times \frac{20}{100} = \frac{120x}{100} = 1.2x$
Now, $1.2x = 45$
$\implies x = \frac{45}{1.2} = 37.50$
Given that, the company $Q$ had earned a profit of $10\%$ on expenditure in $2014.$
Let the expenditure of company $Q$ in $2014$ be $₹ x.$
The company $Q$ earn $10\%$ profit on it’s expenditure and this profit adds to the revenue of company $Q.$
Now, $y+y\times \frac{10}{100} = 37.50$
$\implies \frac{110y}{100} = 37.50$
$\implies \frac{11y}{10} = 37.50$
$\implies 11y = 375 . 0$
$\implies y = \frac{375.0}{11} = 34.0909 \approx ₹ 34.1$
$\textbf{Short Method:}$ Let the revenue of company $Q$ in $2014$ be $₹ 100.$
Then the revenue of company $Q$ in $2015 = ₹ 120$
- $120 \longrightarrow 45$
- $100 \longrightarrow 37.50$
The company $Q$ earn $10\%$ profit on its expenditure and this profit adds to the revenue of company $Q.$
Let the expenditure of company $Q$ in $2014$ be $₹ y.$
$\frac{110y}{100} = 37.50$
$\implies y = ₹ 34.1$
So, the correct answer is $(C).$