A starts some business with Rs. 50,000. After 3 months B joins him with Rs. 70,000. At the end of the year, in what ratio should they share the profits?

Answer

To solve the problem of how A and B should share the profits from their business, we will follow these steps:

### Step 1: Determine the investment of A and B
- A starts the business with Rs. 50,000.
- B joins after 3 months with Rs. 70,000.

### Step 2: Calculate the time of investment for each partner
- A invests for the entire year (12 months).
- B invests for the remaining 9 months (since he joins after 3 months).

### Step 3: Calculate the effective capital contribution
- A's effective capital contribution is calculated as:
\[ \text{A's contribution} = \text{Investment} \times \text{Time} = 50,000 \times 12 = 600,000 \]
- B's effective capital contribution is calculated as:
\[ \text{B's contribution} = \text{Investment} \times \text{Time} = 70,000 \times 9 = 630,000 \]

### Step 4: Find the ratio of their contributions
- Now we need to find the ratio of A's and B's contributions:
\[ \text{Ratio} = \frac{600,000}{630,000} \]
- To simplify this ratio, we can divide both numbers by 30,000:
\[ \text{Ratio} = \frac{20}{21} \]

### Conclusion
- Therefore, A and B should share the profits in the ratio of 20:21.