If the investment of company A in 2007 and 2008 were equal, what is the difference between the profit earned in the two years if the income in 2008 was Rs. 24 lakh?

Answer: Option A

Let the investment of A in 2008 be Rs. $$x$$. Then,
$$\begin{array}{rl}& \left(\frac{160}{100}\times x\right)=24\text{ lakh}\\ & \Rightarrow x=\left(24\times \frac{5}{8}\right)\text{lakh}\\ & \Rightarrow x=15\text{ lakh}\end{array}$$
∴ Investment of A in 2008 = 15 lakh
Profit of A in 2008
= Rs. (24 - 15) lakh
= Rs. 9 lakh
Investment of A in 2007
= Investment of A in 2008
= Rs. 15 lakh
Profit of A in 2007
$$\begin{array}{rl}& =\text{Rs.}\left(\frac{45}{100}\times 15\text{ lakh}\right)\\ & =\text{Rs.}\frac{27}{4}\text{ lakh}\\ & =\text{Rs. 6.75 lakh}\end{array}$$
Difference between the profits of A in 2007 and 2008
= Rs. (9 - 6.75) lakh
= Rs. 2.25 lakh