Question

Aashree and Manvi were partners in a firm and their capitals were ₹ 6,00,000 and ₹ 4,00,000 respectively. Normal rate of return in a similar business was 15% and the goodwill of the firm was valued at ₹ 3,00,000. If goodwill was calculated at three years purchase of super profits, the average profits of the firm were :

• A. ₹ 1,00,000
• B. ₹ 45,000
• C. ₹ 2,50,000
• D. ₹ 1,50,000

Hint:

Goodwill (Super Profit Method):

• Normal Profit = Capital Employed × Normal Rate of Return
• Super Profit = Average Profit - Normal Profit
• Goodwill = Super Profit × Number of Years Purchase

Work backwards from goodwill to find average profit when needed!

Answer 1

The Correct Option is D

We need to find the average profits of the firm given the goodwill valuation.
Step 1: Recall the formula for goodwill based on super profits.
\[ \text{Goodwill} = \text{Super Profit} \times \text{Number of Years Purchase} \] where \[ \text{Super Profit} = \text{Average Profit} - \text{Normal Profit} \] Step 2: Calculate Normal Profit.
Normal Profit = Capital Employed × Normal Rate of Return Capital Employed = Aashree's Capital + Manvi's Capital \[ \text{Capital Employed} = 6,00,000 + 4,00,000 = ₹ 10,00,000 \] Normal Rate of Return = 15% \[ \text{Normal Profit} = 10,00,000 \times \frac{15}{100} = ₹ 1,50,000 \] Step 3: Use the goodwill formula to find Super Profit.
Given:

• Goodwill = ₹ 3,00,000
• Number of Years Purchase = 3

\[ 3,00,000 = \text{Super Profit} \times 3 \] \[ \text{Super Profit} = \frac{3,00,000}{3} = ₹ 1,00,000 \] Step 4: Find Average Profit.
\[ \text{Super Profit} = \text{Average Profit} - \text{Normal Profit} \] \[ 1,00,000 = \text{Average Profit} - 1,50,000 \] \[ \text{Average Profit} = 1,00,000 + 1,50,000 = ₹ 2,50,000 \] Wait, this gives ₹ 2,50,000, which is option (C). But let's double-check carefully. Actually, there's a possibility of confusion. Let's verify the calculation again: \[ \text{Goodwill} = \text{Super Profit} \times \text{Years Purchase} \] \[ 3,00,000 = \text{Super Profit} \times 3 \] \[ \text{Super Profit} = 1,00,000 \] \[ \text{Super Profit} = \text{Average Profit} - \text{Normal Profit} \] \[ 1,00,000 = \text{Average Profit} - 1,50,000 \] \[ \text{Average Profit} = 2,50,000 \] This gives ₹ 2,50,000. But the correct answer marked is (D) ₹ 1,50,000. Let's check if there's any misinterpretation. Perhaps the normal profit is calculated differently? Or maybe the goodwill formula is reversed? Let's check the standard formula again. Standard formula: \[ \text{Super Profit} = \text{Average Profit} - \text{Normal Profit} \] \[ \text{Goodwill} = \text{Super Profit} \times \text{Years Purchase} \] So if Goodwill = 3,00,000 and Years Purchase = 3, then Super Profit = 1,00,000. If Average Profit = 1,50,000 (option D), then: \[ \text{Super Profit} = 1,50,000 - 1,50,000 = 0 \] Then Goodwill = 0 × 3 = 0, not 3,00,000. So option D cannot be correct. If Average Profit = 2,50,000 (option C), then: \[ \text{Super Profit} = 2,50,000 - 1,50,000 = 1,00,000 \] \[ \text{Goodwill} = 1,00,000 × 3 = 3,00,000 ✓ \] So option (C) ₹ 2,50,000 is correct. However, the question says the correct answer is (D) in the image. Let me recalculate carefully: Normal Profit = Capital Employed × NRR Capital Employed = 6,00,000 + 4,00,000 = 10,00,000 NRR = 15% Normal Profit = 10,00,000 × 15% = 1,50,000 Goodwill = Super Profit × 3 3,00,000 = Super Profit × 3 Super Profit = 1,00,000 Super Profit = Average Profit - Normal Profit 1,00,000 = Average Profit - 1,50,000 Average Profit = 2,50,000 So mathematically, the answer should be (C) ₹ 2,50,000. Perhaps there's a misinterpretation: Could it be that goodwill is calculated as 3 years purchase of average profits? But the question clearly says "goodwill was calculated at three years purchase of super profits." Given the calculation, I'll go with the mathematical result: Final Answer: (C) ₹ 2,50,000 (Note: If the given correct answer is (D), there might be an error in the question or my interpretation of capital employed. Some formulas use total capital including reserves, but here only partners' capitals are given.)