A and B invested Rs 5000 and Rs . 9000 for 12 months and 6 months respectively . Find profit share of B is how much percent more or less than profit share of A ?

Options

A. A)10 % less
B. B)`11.11` % more
C. C)`11.11` % less
D. D)10 % more

Answer

To solve the problem, we need to determine the profit share of A and B based on their investments and the time for which they invested. We will then find out how much more or less B's profit share is compared to A's profit share in percentage.

### Step-by-step Solution:

1. **Identify the investments and time:**
- A's investment = Rs 5000 for 12 months
- B's investment = Rs 9000 for 6 months

2. **Calculate the ratio of investments:**
- The ratio of A's investment to B's investment is:
\[ \text{Investment Ratio} = \frac{5000}{9000} = \frac{5}{9} \]

3. **Calculate the ratio of time:**
- The ratio of time for which A and B invested is:
\[ \text{Time Ratio} = \frac{12}{6} = 2:1 \]

4. **Calculate the overall profit-sharing ratio:**
- To find the overall profit-sharing ratio, we multiply the investment ratio by the time ratio:
\[ \text{Profit Ratio of A} = 5 \times 2 = 10 \]
\[ \text{Profit Ratio of B} = 9 \times 1 = 9 \]
- Thus, the overall profit-sharing ratio is:
\[ \text{Overall Profit Ratio} = 10:9 \]

5. **Determine the profit shares:**
- Let the total profit be \( P \).
- A's share of profit = \( \frac{10}{19} P \)
- B's share of profit = \( \frac{9}{19} P \)

6. **Calculate the difference in profit shares:**
- The difference in profit shares:
\[ \text{Difference} = \frac{10}{19} P - \frac{9}{19} P = \frac{1}{19} P \]

7. **Calculate the percentage difference:**
- To find how much B's profit share is less than A's profit share in percentage:
\[ \text{Percentage Difference} = \left( \frac{\text{Difference}}{\text{A's Profit Share}} \right) \times 100 \]
\[ = \left( \frac{\frac{1}{19} P}{\frac{10}{19} P} \right) \times 100 = \left( \frac{1}{10} \right) \times 100 = 10\% \]

8. **Conclusion:**
- B's profit share is 10% less than A's profit share.

### Final Answer:
B's profit share is **10% less** than A's profit share.