Reverse Goodwill Problems: Find the Missing Figure Without Guesswork

Goodwill questions usually begin in a comfortable way. The question gives profits, capital employed, normal rate of return, and years’ purchase. You calculate goodwill.

Reverse goodwill problems feel different.

Here, goodwill is already given. The question asks you to find something hidden behind it: average profit, super profit, capital employed, or normal rate of return. At first, it may feel like the question is moving backwards.

But that is exactly the point. A reverse goodwill problem is not a new method. It is the same goodwill formula used in the opposite direction.

Once you learn how to turn the formulas around, these questions become some of the easiest goodwill numericals to score.

What Makes a Goodwill Problem “Reverse”?

A normal goodwill question asks:

Given profit, capital, rate, and years' purchase, find goodwill.

A reverse goodwill question asks:

Given goodwill and some other figures, find the missing profit, capital, or rate.

For example:

Goodwill is valued at Rs. 90,000 at 3 years' purchase of super profit.
Capital employed is Rs. 5,00,000 and normal rate of return is 12%.
Find the average profit.

The question has not changed the chapter. It has only changed the unknown.

Instead of moving from average profit to goodwill, you move from goodwill back to super profit, then back to average profit.

The First Reading Rule

Before you calculate anything, identify the method.

Most reverse goodwill mistakes happen because students see the given goodwill and immediately divide or multiply without reading the method line.

Look for these words:

Wording in the question	Method being used
”years’ purchase of average profit”	Average profit method
”years’ purchase of super profit”	Super profit method
”capitalisation of average profit”	Capitalisation of average profit
”capitalisation of super profit”	Capitalisation of super profit

Each method has a different path back to the missing figure.

Keep These Base Formulas Ready

Reverse questions become simple when your base formulas are clear.

Average Profit Method

Goodwill = Average profit x Years' purchase

So:

Average profit = Goodwill / Years' purchase

Super Profit Method

Goodwill = Super profit x Years' purchase

Super profit = Average profit - Normal profit

Normal profit = Capital employed x Normal rate of return / 100

So:

Super profit = Goodwill / Years' purchase

Then use the missing part of:

Super profit = Average profit - Normal profit

Capitalisation of Average Profit

Capitalised value = Average profit x 100 / Normal rate of return

Goodwill = Capitalised value - Capital employed

So:

Capitalised value = Goodwill + Capital employed

Capitalisation of Super Profit

Goodwill = Super profit x 100 / Normal rate of return

So:

Super profit = Goodwill x Normal rate of return / 100

or:

Normal rate of return = Super profit x 100 / Goodwill

The Reverse Goodwill Route Map

Use this quick map before solving.

Missing figure	First figure to find	Then find
Average profit under super profit method	Super profit	Normal profit, then average profit
Capital employed under super profit method	Super profit	Normal profit, then capital employed
Normal rate of return under super profit method	Super profit	Normal profit, then rate
Average profit under capitalisation method	Capitalised value	Average profit
Capital employed under capitalisation method	Capitalised value	Capital employed
Normal rate of return under capitalisation method	Capitalised value	Rate

The secret is not speed. The secret is sequence.

Case 1: Finding Missing Average Profit

Let us start with a super profit method question.

Goodwill of a firm is Rs. 90,000. It is valued at 3 years’ purchase of super profit. Capital employed is Rs. 5,00,000 and normal rate of return is 12%. Find the average profit.

Step 1: Find Super Profit

Goodwill = Super profit x Years' purchase

Rs. 90,000 = Super profit x 3

Super profit = Rs. 90,000 / 3
             = Rs. 30,000

Step 2: Find Normal Profit

Normal profit = Capital employed x Normal rate of return / 100

Normal profit = Rs. 5,00,000 x 12 / 100
              = Rs. 60,000

Step 3: Find Average Profit

Super profit = Average profit - Normal profit

Rs. 30,000 = Average profit - Rs. 60,000

Average profit = Rs. 30,000 + Rs. 60,000
               = Rs. 90,000

So, the average profit is Rs. 90,000.

This common sense check helps you catch errors. If your answer for average profit is lower than normal profit, but goodwill is positive, something is wrong.

Case 2: Finding Missing Capital Employed

Now let us reverse the formula in another direction.

Goodwill is Rs. 75,000, valued at 3 years’ purchase of super profit. Average profit is Rs. 1,05,000 and normal rate of return is 10%. Find capital employed.

Step 1: Find Super Profit

Super profit = Goodwill / Years' purchase

Super profit = Rs. 75,000 / 3
             = Rs. 25,000

Step 2: Find Normal Profit

Super profit = Average profit - Normal profit

Rs. 25,000 = Rs. 1,05,000 - Normal profit

Normal profit = Rs. 1,05,000 - Rs. 25,000
              = Rs. 80,000

Step 3: Find Capital Employed

Normal profit = Capital employed x Normal rate of return / 100

Rs. 80,000 = Capital employed x 10 / 100

Capital employed = Rs. 80,000 x 100 / 10
                 = Rs. 8,00,000

So, capital employed is Rs. 8,00,000.

This is the most common wrong turn in reverse goodwill problems.

Case 3: Finding Missing Normal Rate of Return

Now suppose the rate is missing.

Goodwill is Rs. 60,000, valued at 2 years’ purchase of super profit. Average profit is Rs. 1,20,000 and capital employed is Rs. 6,00,000. Find the normal rate of return.

Step 1: Find Super Profit

Super profit = Goodwill / Years' purchase

Super profit = Rs. 60,000 / 2
             = Rs. 30,000

Step 2: Find Normal Profit

Super profit = Average profit - Normal profit

Rs. 30,000 = Rs. 1,20,000 - Normal profit

Normal profit = Rs. 1,20,000 - Rs. 30,000
              = Rs. 90,000

Step 3: Find Normal Rate of Return

Normal profit = Capital employed x Normal rate of return / 100

Rs. 90,000 = Rs. 6,00,000 x Rate / 100

Rate = Rs. 90,000 x 100 / Rs. 6,00,000
     = 15%

So, the normal rate of return is 15%.

Check it once:

Normal profit = Rs. 6,00,000 x 15 / 100
              = Rs. 90,000

Super profit = Rs. 1,20,000 - Rs. 90,000
             = Rs. 30,000

Goodwill = Rs. 30,000 x 2
         = Rs. 60,000

The check brings you back to the given goodwill, so the answer is consistent.

Case 4: Reverse Capitalisation of Average Profit

Capitalisation questions feel harder because they use business value in between.

Remember the key idea:

Goodwill = Capitalised value - Capital employed

So if goodwill is given:

Capitalised value = Goodwill + Capital employed

Once you have capitalised value, the missing figure can be found.

Example: Find Average Profit

Goodwill is Rs. 2,00,000. Capital employed is Rs. 8,00,000 and normal rate of return is 12%. Find the average profit under capitalisation of average profit method.

Step 1: Find Capitalised Value

Capitalised value = Goodwill + Capital employed

Capitalised value = Rs. 2,00,000 + Rs. 8,00,000
                  = Rs. 10,00,000

Step 2: Find Average Profit

Capitalised value = Average profit x 100 / Normal rate of return

Rs. 10,00,000 = Average profit x 100 / 12

Average profit = Rs. 10,00,000 x 12 / 100
               = Rs. 1,20,000

So, average profit is Rs. 1,20,000.

Case 5: Finding Capital Employed in Capitalisation Method

Goodwill is Rs. 2,00,000. Average profit is Rs. 1,50,000 and normal rate of return is 15%. Find capital employed under capitalisation of average profit method.

Step 1: Find Capitalised Value

Capitalised value = Average profit x 100 / Normal rate of return

Capitalised value = Rs. 1,50,000 x 100 / 15
                  = Rs. 10,00,000

Step 2: Find Capital Employed

Goodwill = Capitalised value - Capital employed

Rs. 2,00,000 = Rs. 10,00,000 - Capital employed

Capital employed = Rs. 10,00,000 - Rs. 2,00,000
                 = Rs. 8,00,000

So, capital employed is Rs. 8,00,000.

The logic is simple: if the business is valued at Rs. 10,00,000 from its profits and Rs. 2,00,000 of that value is goodwill, the remaining Rs. 8,00,000 is capital employed.

Case 6: Finding Normal Rate in Capitalisation Method

Goodwill is Rs. 3,00,000. Capital employed is Rs. 9,00,000 and average profit is Rs. 1,80,000. Find the normal rate of return under capitalisation of average profit method.

Step 1: Find Capitalised Value

Capitalised value = Goodwill + Capital employed

Capitalised value = Rs. 3,00,000 + Rs. 9,00,000
                  = Rs. 12,00,000

Step 2: Find Normal Rate of Return

Capitalised value = Average profit x 100 / Normal rate of return

Rs. 12,00,000 = Rs. 1,80,000 x 100 / Rate

Rate = Rs. 1,80,000 x 100 / Rs. 12,00,000
     = 15%

So, the normal rate of return is 15%.

Case 7: Reverse Capitalisation of Super Profit

Capitalisation of super profit uses this formula:

Goodwill = Super profit x 100 / Normal rate of return

This means:

Super profit = Goodwill x Normal rate of return / 100

Example: Find Super Profit

Goodwill is Rs. 1,80,000 and normal rate of return is 12%. Find super profit under capitalisation of super profit method.

Super profit = Goodwill x Normal rate of return / 100

Super profit = Rs. 1,80,000 x 12 / 100
             = Rs. 21,600

So, super profit is Rs. 21,600.

If the question also gives capital employed, you can then calculate normal profit and average profit.

Normal profit = Capital employed x Normal rate of return / 100

Average profit = Normal profit + Super profit

This is why reverse goodwill questions often feel like a chain. One figure unlocks the next.

How to Avoid Formula Confusion

Use this three-question test before writing the answer.

1. Is Years’ Purchase Given?

If years’ purchase is given, the question usually belongs to average profit method or super profit method.

Goodwill = Profit base x Years' purchase

The profit base may be average profit or super profit, depending on the wording.

2. Is Normal Rate of Return Given?

If normal rate of return is given, the question may involve normal profit or capitalisation.

Do not assume the method only from the rate. Read whether the question says “years’ purchase” or “capitalisation”.

3. Is Capital Employed Given or Missing?

If capital employed is given, it may help you calculate normal profit.

If capital employed is missing, you will probably have to find normal profit first, then use:

Capital employed = Normal profit x 100 / Normal rate of return

A Compact Working Note Format

Use the same working note pattern every time.

Method:
Given goodwill:
Formula used:
Step 1:
Step 2:
Step 3:
Check:

For example:

Method: Super profit method
Given goodwill: Rs. 75,000
Formula used: Goodwill = Super profit x Years' purchase
Step 1: Super profit = Rs. 75,000 / 3 = Rs. 25,000
Step 2: Normal profit = Average profit - Super profit
Step 3: Capital employed = Normal profit x 100 / Rate
Check: Goodwill = Super profit x Years' purchase

This format looks simple, but it keeps your answer readable and reduces careless mistakes.

Common Mistakes in Reverse Goodwill Problems

Mistake	Why it causes trouble
Dividing goodwill by rate when years’ purchase is given	It mixes two different methods
Treating normal profit and average profit as the same	Super profit disappears from the calculation
Forgetting to add capital employed to goodwill in capitalisation of average profit	Capitalised value becomes wrong
Writing rate as an amount instead of a percentage	The final answer loses meaning
Skipping the final check	A small sign error remains hidden

The best protection is to write formulas with labels. Do not write only numbers.

Final Check Before You Move On

At the end of every reverse goodwill question, test your answer by going forward again.

If you found average profit, use it to calculate super profit and goodwill.

If you found capital employed, use it to calculate normal profit, super profit, and goodwill.

If you found normal rate of return, use it to calculate normal profit, super profit, and goodwill.

If the final goodwill matches the goodwill given in the question, your working is likely correct.

Reverse goodwill problems are not about guessing the examiner’s trick. They are about respecting the formula chain.

Start with the method. Move one link at a time. Check by returning to the given goodwill.

That is the whole game.

Frequently Asked Questions

What is a reverse goodwill problem?

A reverse goodwill problem gives the value of goodwill and asks you to find another figure, such as average profit, super profit, capital employed, or normal rate of return. You use the usual goodwill formula backwards.

Which formula should I write first?

Write the formula for the method mentioned in the question. If the question says years’ purchase of super profit, start with Goodwill = Super profit x Years' purchase. If it says capitalisation of average profit, start with Goodwill = Capitalised value - Capital employed.

How do I find average profit when goodwill is given?

First identify the method. Under average profit method, divide goodwill by years’ purchase. Under super profit method, first find super profit, then add normal profit to it.

How do I find capital employed when goodwill is given?

Under super profit method, find super profit first, then normal profit, then use Capital employed = Normal profit x 100 / Normal rate of return. Under capitalisation of average profit, find capitalised value and subtract goodwill.

How do I find normal rate of return?

Find normal profit first. Then use Normal rate of return = Normal profit x 100 / Capital employed. If the question uses capitalisation of average profit, first find capitalised value by adding goodwill and capital employed.

Why do I need to check the answer again?

Because reverse questions can hide small sign and substitution errors. If your calculated figure gives back the same goodwill when you use the formula normally, your answer is much safer.