Question

P and Q are partners in a firm. P is entitled to a salary of ₹7,500 p.m. and a commission of 10% of net profit before charging any commission. Q is entitled to a commission of 10% of net profit after charging his commission. Net profit for the year ended 31st March 2024 was ₹2,20,000. Show the distribution of profit.

Hint:

When distributing profit, always consider salaries, commissions, and the agreed-upon profit-sharing ratio before distributing the remaining profit.

Answer 1

Step 1: Understanding the profit-sharing arrangement.
- P is entitled to a salary of ₹7,500 per month, and commission of 10% of the net profit before charging any commission. - Q is entitled to a commission of 10% of the net profit after charging his commission. - The total net profit for the year is ₹2,20,000.
Step 2: Calculation of P’s salary and commission.
P’s salary for the year: \[ 7,500 \times 12 = 90,000 \] Now, P is entitled to 10% commission on net profit before commission. Let’s assume the total net profit before P’s commission is ₹x. P’s commission is: \[ \text{P’s commission} = 0.10x \] Therefore, the total net profit is the sum of the net profit before commission (₹x), P’s salary (₹90,000), and P’s commission (0.10x). Hence: \[ x = 2,20,000 + 90,000 = 3,10,000 \] P’s commission will be: \[ 0.10 \times 3,10,000 = 31,000 \] Step 3: Calculation of Q’s commission.
Q’s commission is 10% of the net profit after his commission. Let’s assume Q’s commission is ₹y. Then, the net profit after charging Q’s commission is: \[ \text{Net profit after Q’s commission} = 2,20,000 - 31,000 - y \] Since Q is entitled to 10% of the net profit after his commission: \[ y = 0.10(2,20,000 - 31,000 - y) \] Solving for \(y\), we get: \[ y = 0.10(1,89,000 - y) \] \[ y = 18,900 - 0.10y \] \[ 1.10y = 18,900 \] \[ y = \frac{18,900}{1.10} = 17,181.82 \] Q’s commission is ₹17,181.82.
Step 4: Distribution of profit.
After P’s salary and commission, and Q’s commission are deducted, the remaining profit is distributed between P and Q based on their agreed ratio. The remaining profit is: \[ 2,20,000 - 90,000 - 31,000 - 17,181.82 = 81,818.18 \] The remaining profit of ₹81,818.18 is shared between P and Q in the agreed ratio. Since the ratio is not specified, we assume it to be 1:1. Thus, P and Q each receive: \[ \frac{81,818.18}{2} = 40,909.09 \] Step 5: Conclusion.
The distribution of profit is:
- P’s salary: ₹90,000
- P’s commission: ₹31,000
- P’s share of remaining profit: ₹40,909.09
- Q’s commission: ₹17,181.82
- Q’s share of remaining profit: ₹40,909.09