P , Q & R started a business with investment of Rs.28000, Rs.16000 & Rs.20000 respectively. After the 6 months P added 25% more of his initial investment and Q withdrew Rs.6000. At the end of the year profit earned by R is Rs.3120, then find the difference between profit share of P and of Q.

The correct answer is Rs.2886.

Step 1: Calculate the effective investment of each partner for the entire year (12 months).

The total equivalent investment for 1 year is calculated by taking the sum of (Investment Amount × Time Period in months) for each partner.

Partner P:

Initial investment for the first 6 months = Rs. 28000

After 6 months, P added 25% more of his initial investment:

Added amount = 25% of 28000 = 0.25 × 28000 = Rs. 7000

New investment for the remaining 6 months = 28000 + 7000 = Rs. 35000

Total equivalent investment of P = (28000 × 6) + (35000 × 6)

$=168000+210000=378000$

Partner Q:

Initial investment for the first 6 months = Rs. 16000

After 6 months, Q withdrew Rs. 6000:

New investment for the remaining 6 months = 16000 - 6000 = Rs. 10000

Total equivalent investment of Q = (16000 × 6) + (10000 × 6)

$=96000+60000=156000$

Partner R:

Investment remained unchanged for the whole 12 months = Rs. 20000

Total equivalent investment of R = 20000 × 12

$=240000$

Step 2: Find the ratio of profit distribution among P, Q, and R.

Ratio of profit (P : Q : R) = 378000 : 156000 : 240000

Dividing by 6000:

P : Q : R = 63 : 26 : 40

Step 3: Calculate the difference between the profit shares of P and Q.

We are given that R's share of profit is Rs. 3120.

Let 1 unit of ratio be $x$.

Share of R = 40 units = 3120

$1\text{unit}=\frac{3120}{40}=78$

Difference between the profit share of P and Q:

Difference in ratio units = 63 - 26 = 37 units

Difference in profit = 37 × 78

$=2886$

Thus, the difference between the profit share of P and Q is Rs.2886.