A and B start a business with capitals of Rs. 20,000 and Rs. 45,000. If the profit is divided in the ratio 2: 3, determine the ratio of the time periods of investment for A and B.

Correct option is B

Given:
Capital of A = Rs 20000
Capital of B = Rs 45000
Profit ratio of A to B = 2 : 3
Formula Used:
Ratio of Profit = (Capital of A × Time of A) : (Capital of B × Time of B)
Solution:
Let the time periods for A and B be represented as variables.
Substitute the given values into the formula:
​$$\frac{20000 × T_A}{45000 × T_B} = \frac{2}{3}$$​​
​$$\frac{4 × T_A}{9 × T_B} = \frac{2}{3}$$​​
​$$\frac{T_A}{T_B} = \frac{2}{3} × \frac{9}{4}$$​​
​$$\frac{T_A}{T_B} = \frac{18}{12}$$​​
​$$\frac{T_A}{T_B} = \frac{3}{2}$$​​
Final Answer
So the correct answer is (b)