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Profiting from profit and loss

Introduction:

Percentage may be one of the most popular mathematical concepts around but as a pure motivating force, it is difficult to beat profit and loss. Such has been their power that for centuries, human beings have done everything from the noble to the utterly dishonest just to make a few dollars more. And it is not just business. In fact, almost all economic activity revolves around the concept of profit. After all, it is impossible to spend more than you earn, is it not?

It is also impossible to take a competitive examination without coming across at least one question on profit and loss. So if you are not too good on profit and loss, you will be incurring a loss in these examinations. Which would be a pity as there is nothing really difficult about profit and loss.

Like most commercial mathematics, profit and loss is fundamentally simple in nature. All one needs is the knowledge of basic mathematical operations, fractions, and percentage. Add lots of common sense to that mixture, and you will be ready to make a neat little profit whenever an exercise on profit and loss comes up.

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Nature of exercises:


  • The rate of profit or loss
     
  • The amount of profit or loss
     
  • The cost price
     
  • The selling price
     
  • The rate or amount of discount offered
     
  • The quantity to be sold or manufactured to make a certain amount of profit or loss

What you need to solve them:


At its very core, profit and loss is dreadfully simple. If the selling price of an article exceeds the cost of making it, a profit is made. If on the other hand, the cost is greater than the selling price, a loss has been incurred. And as we all now, discounts are basically reductions in selling price to boost sales. It is as basic as that.

The formulae that are going to come into play are as follows:

  • Profit = Selling price - Cost price
     
  • Loss = Cost price - Selling price
     
  • Discount = Selling price - amount of discount
     
  • Profit per cent = [Profit/ Cost price] x 100
     
  • Loss per cent = [Loss / Cost price] x 100
     
  • Discount per cent = [Discount/ Selling price] x 100
     
  • Selling price = Cost price x [100 + profit per cent] / 100, if there has been a profit.
     
  • Selling price = Cost price x [100 - Loss per cent] /100, if there has been a loss.
     
  • Cost price = Selling price x [100/ 100 + Profit per cent], if there has been a profit
     
  • Cost price = Selling price x [100/ 100 - Loss per cent], if there has been a loss.
     
  • Discounted price = Selling price x [100 - Discount per cent] / 100
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Some strategies:


  • As there are basically five terms involved in these questions - profit, loss, discount, cost price and selling price - I always found that it helped me immensely to keep five slots mentally prepared for them and slip the amounts or rates concerned into these slots. Believe me, if you can remember your basic information, half the work is done.
  • A terrific way to prepare for these exercises is to mentally work out the amounts and rates of discounts whenever you come across an advertisement for a discount sale in a newspaper or periodical. Also work out how much you gain from a discount - that is your profit. Similarly, the next time you hear of a price increase, just try to figure out how much you are losing. As I mentioned earlier, profit and loss are a part of our lives. If you get accustomed to calculating them, questions on profit and loss will not pose any problems to you.
  • There is no substitute for memorising the formulae. Some smart alecks claim that remembering a single formula is enough as the others are derived from it. The fact is that you do not have time to sit about deriving formulae in the examination hall. Formulae are mugging up territory. Fortunately, there are not too many of them to remember.

Points to keep in mind:


  • Profit and loss per cent is ALWAYS computed by dividing the profit or loss made by the cost price. I know that sounds elementary and yet candidates quite often stumble into the error of basing the profit or loss on the selling price. It is only discount which is calculated on selling price.
  • Sometimes questions mention more than one discount on the same article. In these cases, calculate the initial rate of discount on the original selling price and the subsequent rate of discount on the selling price minus the original discount. See the sample questions in this regard.
  • Occasionally, questions make a reference to 'marked price'. Do not let this confuse you - it is in fact the selling price. Marked price quite literally means the price marked on the article and that is the selling price. Similarly, 'gain' is the same as profit.
  • Do remember to distinguish between the quantity of profit or loss and profit or loss expressed in terms of percentage. It has been observed that people sometimes mix up the two concepts. For instance, if a question mentions that a person made a 10% loss on the sale of an article costing Rs 45, many times candidates simply subtract 10 from 45, forgetting that 10 is actually a percentage figure! This is an error that creeps in when one works in a hurry, so be careful.
  • As percentage is an intrinsic part of questions on profit and loss, the points that need to be kept in mind while handling percentage exercises need to be kept in mind here as well. To view them, click here (link to 'Points to keep in mind' section of percentage)
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Sample questions with solutions:



1. A sold his watch for Rs 190, thus bearing a loss of 5%. The cost price of the article is

a. Rs 237.50 b. Rs. 220 c. Rs. 210 d. Rs. 200 e. None of these

Solution:

1. What you need to find here is the cost price. You are given the rate of loss and the selling price.

2. Now, cast your mind back to the formulae mentioned in the 'What you need to know' section. The formula for determining the cost price when a loss has been incurred is = Selling price x [100/ 100 - Loss per cent],

3. Inserting the values of loss and selling price in this formula, we get,

Cost price = Rs.190 x [100/100-5]
Cost price = Rs.190 x [100/95]
Cost price = Rs. 200

The cost of the article is Rs. 200 and the correct answer is d.

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2. A man sells two shirts for Rs. 990 each. On one he gains 10% and on the other he loses 10%. What is his total gain or loss?

a. 1% gain b. 1% loss c. No gain or loss d. 5% gain

Solution:

1. Now, do not go rushing in and assume that as the selling price is the same and the profit and loss rates are equal as well, the profit and loss would have cancelled each other out and the man makes neither a profit or a loss. Things are not as simple as that here.

2. Here we have been given two selling prices and the rates of profit [gain] and loss. What we need to find is whether the transaction yielded the person a gain or loss.

3. First we need to find the cost price of the two shirts. Using the formula for determining cost price, we get Cost of the shirt on which a profit was made = Selling price x [100/ 100 + Profit per cent], or 990x [100/110] = Rs.900 Cost of the shirt on which a loss was made = Selling price x (100/ 100 - Loss per cent), or 990 x [100/90] = Rs.1100

4. Therefore the total cost of producing the two shirts is Rs [1100 + 900] = Rs.2000

5. But the total selling price of the two shirts is = Rs. [990 + 990] = Rs 1980

6. As the cost price is greater than the selling price, a loss has been incurred. This loss is equal to Rs. [2000 -1980] = Rs. 20

7. To calculate the percentage of the loss, we use the formula [Loss / Cost price] x 100, or [20/2000] x 100 = 1%.

So the man made a loss of 1% and the correct answer is b.

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3. Peter bought 2000 bananas at Rs 9 per dozen. He sold some of them for Rs. 1 each and the remainder at Rs. 0.80 each. He made a profit of Rs. 150. How many bananas did he sell at Rs.1 each?

a. 550 b. 600 c. 50 d.250

Solution:

1. Here we have been given the cost price, the selling prices and the amount of profit. What we need to find is the quantity sold at a particular price.

2. The cost of bananas is Rs 9 per dozen. So the cost of a single banana would be Rs. [9/12] or Rs. 0.75.

3. So, the cost of 200 bananas would be = Rs. [2000 x 0.75] = Rs. 1500

4. Now, Peter being an astute businessman, made a profit of Rs 150. So the total selling price of the bananas must have been = Rs. [1500 + 150] = Rs. 1650

5. So, if the number of bananas sold for Rs 1 each is b, then the bananas sold at Rs. 0.80 would be 2000 - b, as there were a total of 2000 bananas,

6. Now, as per the conditions given in the question

[b x 1] + [2000 - b] x 0.80 = Rs. 1650
b+1600-0.80b = 1650
0.20 b= [1650-1600]
0.20b = 50
b= 50 /0.20 or 5000/20
b=250

Peter sold 250 bananas as Rs 1 each and the remaining 1750 at Rs.0.80 each. The correct answer is d.

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4. Two successive discounts, the first of 20% and the second of 25% are equivalent to a single discount of

a. 22 ½% b. 36% c.40% d.45%
[RBI exam, 1980]

Solution:

First of all, do not make the mistake of simply adding the two rates of discounts and arriving at 45%. This is because the second rate of discount was offered on the selling price, which had been reduced by the earlier discount.

Now, let us assume that the selling price of the article mentioned is Rs. 100. Why Rs. 100? Well, because it is easier to calculate percentages on an assumed price of Rs. 100 and also because using algebra would be really messy here.

So, if the selling price is Rs. 100, the price after the first discount would be = Selling price x [100 - Discount per cent] / 100 or, 100 x [100-20] /100 = Rs. 80

Rs. 80 would be price at which the second discount would have been given. So the selling price after the second discount would be = Selling price x [100 - Discount per cent] / 100 or 80 x (100-25)/100 = Rs. 60.

Now, the selling price after the two discounts is Rs. 60. So a single rate of discount equal to the two discounts would be = [Discount/ Selling price] x 100 or [100-60] /100 x 100 = 40%

A single discount of 40% would thus be equal to successive discounts of 20% and 25%. The correct answer is c.

Send us a question


Is there a profit and loss -based question that you cannot solve? Or a question that you would like to share with other candidates? If so, then do mail them to us, along with details of the examination paper / sample paper in which you found them. We will try to solve them and send the solution to you. Any questions that you send will also be uploaded to the Sample Questions section of the web site and you will be given credit for contributing them.

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Questions on profit and loss are always descriptive in nature. These inevitably revolve around the determination of: 

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