P started the business with an investment of Rs.12000. After x months...
To solve this problem, let's break it down step by step:
1. Let's assume that P started the business with an investment of Rs. 12,000.
2. After x months, Q joined the business and invested Rs. 3,000 more than P.
3. Therefore, the investment of Q can be represented as Rs. 12,000 + Rs. 3,000 = Rs. 15,000.
4. Now, let's calculate the profit share of P. We are given that the total profit is Rs. 11,000 and the profit share of P is Rs. 6,000.
5. Let P's investment run for the entire year, which is 12 months.
6. Since the profit share is directly proportional to the time period, we can set up the following proportion:
P's investment / Q's investment = P's profit share / Q's profit share
Rs. 12,000 / Rs. 15,000 = Rs. 6,000 / Q's profit share
7. Solving for Q's profit share:
Rs. 12,000 / Rs. 15,000 = Rs. 6,000 / Q's profit share
Q's profit share = (Rs. 15,000 * Rs. 6,000) / Rs. 12,000
Q's profit share = Rs. 7,500
8. Now, let's calculate the profit share of Q for x months. Since P's investment is running for the entire year, Q's investment is running for the remaining months, which is (12 - x) months.
Q's profit share for x months = (Rs. 7,500 * x) / 12
9. Since the total profit share is Rs. 11,000, we can set up the following equation:
P's profit share + Q's profit share for x months = Rs. 11,000
Rs. 6,000 + (Rs. 7,500 * x) / 12 = Rs. 11,000
10. Solving for x:
(Rs. 7,500 * x) / 12 = Rs. 11,000 - Rs. 6,000
(Rs. 7,500 * x) / 12 = Rs. 5,000
Rs. 7,500 * x = Rs. 5,000 * 12
Rs. 7,500 * x = Rs. 60,000
x = Rs. 60,000 / Rs. 7,500
x = 8
Therefore, the value of x is 8. Hence, the correct answer is option A.