Lokesh starts a business with Rs 240000. After 3 months Vishal joins him with Rs 210000. At the end of the year what will be the ratio of their profit?

Options

A. `32 : 21`
B. ` 16 : 13`
C. `8 : 5`
D. `45 : 39`

Answer

To find the ratio of profits between Lokesh and Vishal at the end of the year, we will follow these steps:

### Step 1: Determine the investment of each partner
- Lokesh invests Rs 240,000.
- Vishal invests Rs 210,000.

### Step 2: Calculate the time of investment for each partner
- Lokesh invests for the entire year (12 months).
- Vishal joins after 3 months, so he invests for 9 months (12 - 3 = 9).

### Step 3: Calculate the effective capital contribution for each partner
- Lokesh's effective capital contribution = Investment × Time = Rs 240,000 × 12 = Rs 2,880,000.
- Vishal's effective capital contribution = Investment × Time = Rs 210,000 × 9 = Rs 1,890,000.

### Step 4: Find the ratio of their effective capital contributions
- The ratio of Lokesh's to Vishal's effective capital contributions = Rs 2,880,000 : Rs 1,890,000.

### Step 5: Simplify the ratio
- To simplify, we can divide both amounts by 30,000:
- Lokesh: 2,880,000 ÷ 30,000 = 96
- Vishal: 1,890,000 ÷ 30,000 = 63
- Therefore, the ratio is 96 : 63.

### Step 6: Further simplify the ratio
- Divide both sides by 3:
- Lokesh: 96 ÷ 3 = 32
- Vishal: 63 ÷ 3 = 21
- Thus, the final ratio of their profits is 32 : 21.

### Final Answer
The ratio of Lokesh's profit to Vishal's profit at the end of the year is **32 : 21**.

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