A and B started a business investing amounts in the ratio of 2 : 3. If A has invested an additional amount of Rs. 10000, their ratio of investment would have been 3 : 2. The amount invested by A was ?

Initial ratio of investments by A and B = 2 : 3
Let their respective investments are 2x and 3x
According to the question,
If A added Rs. 10000 to his investment
Then the new ratio = 3 : 2
$$\eqalign{ & \Rightarrow \frac{{2x + 10000}}{{3x}} = \frac{3}{2} \cr & \Rightarrow 4x + 20000 = 9x \cr & \Rightarrow 5x = 20000 \cr & \Rightarrow x = 4000 \cr} $$
Original investment by A = 2 × 4000 = Rs. 8000