Question

Find the ratio of investment of Ajay to Vijay if Ajay invests after 6 months of Vijay’s investment and Vijay invests after 3 months of commencement of business. It is known that their profit – sharing ratio after 1 year of commencement of business is 2:3.

• A. 2 : 1
• B. 1 : 3
• C. 3 : 1
• D. 4 : 1

Hint:

Always calculate the "active" time the money was in the business. "After 6 months" means you subtract that time from the remaining duration.

Answer 1

The Correct Option is A

Concept: Profit Ratio = (Investment of A \(\times\) Time of A) : (Investment of V \(\times\) Time of V).
Step 1: Determine the time period for each investment.
Business duration = 12 months.
Vijay starts after 3 months, so his money is invested for \(12 - 3 = 9 \text{ months}\).
Ajay starts 6 months after Vijay, so his money is invested for \(9 - 6 = 3 \text{ months}\).

Step 2: Set up the profit ratio equation.
Let investments be \(I_a\) and \(I_v\). \[ \frac{I_a \times 3}{I_v \times 9} = \frac{2}{3} \] \[ \frac{I_a}{3I_v} = \frac{2}{3} \quad \Rightarrow \quad \frac{I_a}{I_v} = \frac{2 \times 3}{3} = \frac{2}{1} \]