P and Q started a business by investing Rs. 8,000 and Rs. 6,000 respectively. After x months, Q withdrew his investment. At the end of the year, Q’s share of profit was Rs. 2,000 out of a total profit of Rs. 6,000. Find the value of x.

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Information Given in the Question:
P's investment = Rs. 8,000 (for full 12 months)
Q's investment = Rs. 6,000 (for x months)
Total profit = Rs. 6,000
Q’s profit share = Rs. 2,000
P’s profit share = Rs. 6,000 - 2,000 = Rs. 4,000
Concept/Formula Used in the Question:
Profit is distributed in the ratio of investment × time
Detailed Explanation:
P’s investment for 12 months = 8000 × 12 = 96000

Q’s investment for x months = 6000 × x = 6000x
Profit ratio = P : Q = 96000 : 6000x

Given:
Q’s share = 2000 and total = 6000

So ratio = 4000 : 2000 = 2 : 1
Now equate:

$$\frac{96000}{6000x} = \frac{2}{1}$$​​

x = $$\frac{96000}{12000}$$​
x = 8