B starts some business by investing Rs 90000. After 4 months, D joins business by investing Rs 80000. At the end of the year, in what ratio will they share the profit?

Options

A. `10:7`
B. `9:4`
C. `27:16`
D. `7:3`

Answer

To solve the problem, we need to calculate the effective capital contribution of both B and D over the time they were invested in the business.

### Step-by-Step Solution:

1. **Identify the investment and time period for B:**
- B invests Rs 90,000 for the entire year (12 months).
- Therefore, the effective capital contribution of B = Investment × Time = 90,000 × 12 = 1,080,000.

2. **Identify the investment and time period for D:**
- D invests Rs 80,000 but joins the business after 4 months. This means D's investment is for 8 months (12 - 4 = 8).
- Therefore, the effective capital contribution of D = Investment × Time = 80,000 × 8 = 640,000.

3. **Calculate the ratio of their contributions:**
- Now we have the effective contributions:
- B's contribution = 1,080,000
- D's contribution = 640,000
- To find the ratio of their contributions, we can express it as:
\[ \text{Ratio} = \frac{B's \ Contribution}{D's \ Contribution} = \frac{1,080,000}{640,000} \]

4. **Simplify the ratio:**
- Dividing both numbers by 80,000 to simplify:
\[ \frac{1,080,000 \div 80,000}{640,000 \div 80,000} = \frac{13.5}{8} \]
- To convert this into whole numbers, we can multiply both sides by 8:
\[ \frac{13.5 \times 8}{8 \times 8} = \frac{108}{64} \]
- Now, simplifying further by dividing both by 4:
\[ \frac{27}{16} \]

5. **Conclusion:**
- The ratio in which B and D will share the profit is 27:16.