Question:medium

The Goodwill of a firm is Rs 30,000, when it is valued at three years' purchase of the super profits of the business. Find the normal rate of return, if the firm's capital employed is Rs 5,00,000 and average profits of last five years were Rs 60,000.

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Super profit = Goodwill / 3 = Rs 10,000. Normal profit = Average profit - Super profit.
Updated On: Oct 1, 2026
  • 5%
  • 10%
  • 15%
  • 20%
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Write the goodwill equation with an unknown rate.
Let the normal rate be $r$ percent. Normal profit is $5{,}00{,}000 \times r/100$. Super profit is $60{,}000$ minus that value.

Step 2: Put the numbers in the goodwill formula.
Goodwill is 3 times super profit, so
\[ 3\left(60{,}000 - 5{,}000\,r\right) = 30{,}000 \]

Step 3: Solve for r.
Divide both sides by 3.
\[ 60{,}000 - 5{,}000\,r = 10{,}000 \]
\[ 5{,}000\,r = 50{,}000 \]
\[ r = 10 \]

Step 4: Test the answer.
With $r = 10$, normal profit is Rs 50,000. Super profit is $60{,}000 - 50{,}000 = 10{,}000$. Goodwill is $3 \times 10{,}000 = 30{,}000$. This matches the question.

Step 5: Conclude.
The other rates fail. At 5% goodwill is Rs 1,05,000. At 15% and 20% the normal profit is at least Rs 75,000, so there is no super profit.
\[ \boxed{10\%} \]

Final Answer:
The normal rate of return is 10%.
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