B starts some business by investing Rs 17000. After 3 months, D joins business by investing Rs 68000. At the end of the year, in what ratio will they share the profit?

Options

A. `3:4`
B. `1: 3`
C. `9:4`
D. `7 : 4`

Answer

To solve the problem of how B and D will share the profit at the end of the year, we need to consider both the amount invested and the time for which the investment was made.

### Step-by-Step Solution:

1. **Identify the investments and time periods:**
- B invests Rs 17,000 at the start of the year.
- D invests Rs 68,000 after 3 months.

2. **Calculate the time of investment:**
- B's investment is for the entire year, which is 12 months.
- D's investment is for 9 months (since he joins after 3 months).

3. **Calculate the effective capital contribution:**
- For B:
\[ \text{Effective Capital of B} = \text{Investment} \times \text{Time} = 17000 \times 12 = 204000 \]
- For D:
\[ \text{Effective Capital of D} = \text{Investment} \times \text{Time} = 68000 \times 9 = 612000 \]

4. **Determine the ratio of their effective capital contributions:**
- The ratio of B's effective capital to D's effective capital is:
\[ \text{Ratio} = \frac{204000}{612000} \]
- Simplifying this ratio:
\[ \text{Ratio} = \frac{204}{612} = \frac{1}{3} \]

5. **Final Ratio of Profit Sharing:**
- Therefore, B and D will share the profit in the ratio of 1:3.

### Conclusion:
B and D will share the profit in the ratio of **1:3**.