A starts a business with X 4000 and B joins him after 3 months with X 16000. Find the ratio of their profits at the end of year.

Options

A. `1:3`
B. `2:3`
C. `1:9`
D. `1:7`

Answer

To solve the problem of finding the ratio of profits between A and B at the end of the year, we can follow these steps:

### Step 1: Determine the time period each partner invested in the business.
- A invests for the entire year (12 months).
- B joins after 3 months, so B invests for 9 months.

### Step 2: Calculate the capital contribution of each partner.
- A's investment = X 4000
- B's investment = X 16000

### Step 3: Calculate the effective capital contribution for each partner.
- A's effective capital contribution = A's investment × A's time of investment
\[ A's effective capital = 4000 \times 12 = 48000 \]

- B's effective capital contribution = B's investment × B's time of investment
\[ B's effective capital = 16000 \times 9 = 144000 \]

### Step 4: Find the ratio of their effective capital contributions.
- The ratio of A's effective capital to B's effective capital is:
\[ \text{Ratio} = A's effective capital : B's effective capital = 48000 : 144000 \]

### Step 5: Simplify the ratio.
- To simplify the ratio, we can divide both sides by 48000:
\[ \frac{48000}{48000} : \frac{144000}{48000} = 1 : 3 \]

### Conclusion:
The ratio of their profits at the end of the year is **1 : 3**.

---