The concept of Profit and Loss is the central pivot of every concept in business and commerce. Profit and Loss is also an important section of the Quantitative Aptitude section of many graduate level competitive exams. In the following section, we will discuss what profit and loss are an Equation Based Questions. We will introduce the concepts of price and the different kinds of price, we will also get to know about the various kinds of formulas that we use to calculate the profit and the loss in any business transaction.

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## Profit And Loss –Â Equation Based Questions

Let us begin by defining all the terms that we will require in solving the equation based questions on profit and loss.

Cost Price: Cost price is the price at which one purchases an article. The price that you pay to purchase an article or a commodity is the cost price or C.P. of that article.

Selling Price: The price at which the owner sells the article is what we call the selling price. We represent it by S.P.

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One might confuseÂ S.P. with C.P. but that is not the case. Cost price is the price at which the seller acquires an article while as S.P. is the price at which they sell it to make a profit or a loss as we will see ahead.

Profit or Gain: If S.P. is greater than the C.P., we say that the seller makes a profit or gain. In other words, if S.P. > C.P. then the transaction results in a profit or gain. The profit or the gain is equal to [S.P. – C.P.] or the difference between the price at which an item was sold to the cost at which it was acquired.

Loss: On the other hand if the S.P. is less than the C.P., then we say that the seller makes or incurs a loss. In terms of symbols, we may write: if S.P. < C.P. then the transaction results in a loss. The loss is equal to [C.P. – S.P.]. If this difference is positive then the transaction has resulted in a loss, if not then it has resulted in a gain.

### Percentage Loss and Gain

The Profit and Loss are often expressed in terms of percentages as given below:

Percentage Gain: [{GainÃ—100}/C.P.]

Similarly, the percentage loss = [{LossÃ—100}/C.P.,]

We can find the S.P. from percentage gain and percentage loss as:

S.P. = [({100 + %Gain}/100)Ã—C.P.]

Also, S.P. = [({1– – %Loss}/100)Ã—C.P.]

We can find the Cost Price from similar formulas as:

Cost Price = [({100 + %Gain}/100)Ã—S.P.]

C.P. = [({1– – %Loss}/100)Ã—S.P.]

## Solved Examples For You

Example 1: A person buys a radio for Rs. 27.50 and sells it for Rs. 28.60. Find the percentage gain or the percentage loss?

A) 2%Â Â Â Â Â Â Â Â Â Â Â Â B) 3%Â Â Â Â Â Â Â Â Â Â Â Â C) 4%Â Â Â Â Â Â Â Â Â Â Â D) 5%

Answer: Since the S.P. = Rs. 28.60 is greater than the C.P. = Rs. 27.50. So, gain = Rs. (28.60 – 27.50) = Rs. 1.10.

Percentage Gain = [{1.10Ã—100}/27.50]% = 4% and hence the correct option is D) 4%

Example 2: A person incurs 5% loss by selling a watch for Rs. 1140. At what price should the watch be sold to earn 5% profit?

A) Rs. 1378Â Â Â Â Â Â Â Â Â Â B) Rs. 1111Â Â Â Â Â Â Â Â Â Â Â C) Rs. 1256Â Â Â Â Â Â Â Â Â Â Â Â Â D) Rs. 1260

Answer: Let the Selling Price be equal to Rs. x. Then, (100 – percentage loss) : (First S.P.) = (100 + percentage gain) =: (second selling price)

Therefore, [(110 – 5)/1140] = [(100 + 5)/x] or x = Rs. 1260.

Example 3: Pure ghee costs Rs. 100 per kg. After adulterating it with vegetable oil mixing Rs. 50 per kg, a shopkeeper sells the mixture at the rate of Rs. 96 per kg, thereby making a profit of 20%. In what ratio does he mix the two?

A) 1: 2Â Â Â Â Â Â Â Â B) 2: 3Â Â Â Â Â Â Â Â Â Â Â C) 3: 2Â Â Â Â Â Â Â Â Â Â D) 4: 3

Answer: Mean cost price = Rs. [(100/120)Ã—96] = Rs. 80 per kg. By the rule of alligation, we have:

The ratio of the mixture = 30 : 20 = 3 : 2. Hence the correct option is C) 3: 2.

Example 4: Khan purchases a pressure cooker at 9/10th of its selling price and sells it at 8% more than its S.P. Find his percentage gain?

A) 20%Â Â Â Â Â Â Â Â Â Â B) 25%Â Â Â Â Â Â Â Â Â C) 30%Â Â Â Â Â Â Â Â Â D) 35%

Answer: Let the S.P. of the pressure cooker be equal to Rs. x. Then, C.P. of the pressure cooker = 9x/10. Also, the receipt =108% of Rs. x and hence we can write: Receipt = 27x/25. In other words, we have gain =

Rs. [27x/25 – 9x/10] = Rs. [(108x – 90x)/100] = Rs. 18x/100.

Ans hence the percentage gain = [{18x/100} Ã— {10/9x} Ã— 100]% = 20%. Hence the correct option is A) 20%.

Example 5: The price of a jewel, passing through three hands, rises on the whole by 65%. If the first and the second sellers earn 20% and 25% profit respectively, find the percentage profit that the third seller earns?

A) 2%Â Â Â Â Â Â Â B) 3%Â Â Â Â Â Â Â Â Â Â C) 33%Â Â Â Â Â Â Â Â Â D) 10%

Answer: Let the original pice of the jewel be Rs. P and let the profit that the third seller earns be x%. Then as per the conditions in the question, we have:

(100 + x)% of 125% of 120% of P = 165% of P.

Thus we have: [(100 + x)Ã—(125)Ã—(120)Ã—P/100Ã—100Ã—100] = [(165/100)Ã—P]

In other words we can say that (100 + x) = [(165Ã—100Ã—100)/125Ã—120] = 110 or we have x = 10%. Therefore the correct option is D) 10%.

## Practice Questions

Q 1: A dealer sells three-fourths of his articles at a gain of 20% and the remaining at cost price. Find the gain that he earns in the whole transaction.

A) 10%Â Â Â Â Â Â Â Â Â Â B) 15%Â Â Â Â Â Â Â Â Â Â Â Â C) 20%Â Â Â Â Â Â Â Â Â Â D) 25%

Ans: B) 15%

Q 2: A man buys a horse and a carriage for Rs. 3000. He sells the horse at a gain of 20% and the carriage at a loss of 10%, thereby gaining 2% on the whole. Find the cost of the horse.

A) Rs. 3600Â Â Â Â Â Â Â Â Â Â B) Rs. 1200Â Â Â Â Â Â Â Â C) Rs. 4400Â Â Â Â Â Â Â Â D) Rs. 4800

Ans: B) Rs. 1200

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