Solved Examples: Profit and Loss | Quantitative for GMAT PDF Download

Basic Definitions and Formulas

• Cost price (C.P.): This is the price at which an article is purchased.
• Selling price (S.P.): This is the price at which an article is sold.
• Profit or Gain: If the selling price is more than the cost price, the difference between them is the profit incurred.

Formula: Profit or Gain = S.P. – C.P.

• Loss: If the selling price is less than the cost price, the difference between them is the loss incurred.

Formula: Loss = Cost price (C.P.) – Selling Price (S.P.)

• Profit or Loss is always calculated on the cost price.
• Marked price: This is the price marked as the selling price on an article, also known as the listed price.
• Discount or Rebate: This is the reduction in price offered on the marked or listed price.

Below is the list of some basic formulas used in solving questions on profit and loss:

• Gain % = (Gain / CP) * 100
• Loss % = (Loss / CP) * 100
• SP = [(100 + Gain%) / 100] * CP
• SP = [(100 – Loss %) / 100]*CP

The above two formulas can be stated as,

If an article is sold at a gain of 10%, then SP = 110% of CP.

If an article is sold at a loss of 10%, then SP = 90% of CP.

• CP = [100 / (100 + Gain%)] * SP
• CP = [100 / (100 – Loss%)] * SP

Profit and Loss: Solved Examples

Question 1: An article is purchased for Rs. 450 and sold for Rs. 500. Find the gain percent.
Solution:
Gain = SP – CP = 500 – 450 = 50.
Gain% = (50/450)*100 = 100/9 %

Question 2: A man sold a fan for Rs. 465. Find the cost price if he incurred a loss of 7%.
Solution:
CP = [100 / (100 – Loss %)] * SP
Therefore, the cost price of the fan = (100/93)*465 = Rs. 500

Question 3: In a transaction, the profit percentage is 80% of the cost. If the cost further increases by 20% but the selling price remains the same, how much is the decrease in profit percentage?
Solution:
Let us assume CP = Rs. 100.
Then Profit = Rs. 80 and selling price = Rs. 180.
The cost increases by 20% → New CP = Rs. 120, SP = Rs. 180.
Profit % = 60/120 * 100 = 50%.
Therefore, Profit decreases by 30%.

Question 4: A man bought some toys at the rate of 10 for Rs. 40 and sold them at 8 for Rs. 35. Find his gain or loss percent.
Solution:
Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.
Selling price of 8 toys = Rs. 35 → SP of 1 toy = Rs. 35/8
Therefore, Gain = 35/8 – 4 = 3/8.
Gain percent = (3/8)/4 * 100 = 9.375%

Question 5: The cost price of 10 pens is the same as the selling price of n pens. If there is a loss of 40%, approximately what is the value of n?
Solution:
Let the price of each pen be Re. 1.
Then the cost price of n pens is Rs. n and the selling price of n pens is Rs. 10.
Loss = n-10.
Loss of 40% → (loss/CP)*100 = 40
Therefore, [(n-10)/n]*100 = 40 → n = 17 (approx)

Question 6: A dishonest merchant sells his grocery using weights 15% less than the true weights and makes a profit of 20%. Find his total gain percentage.
Solution:
Let us consider 1 kg of grocery bag. Its actual weight is 85% of 1000 gm = 850 gm.
Let the cost price of each gram be Re. 1. Then the CP of each bag = Rs. 850.
SP of 1 kg of bag = 120% of the true CP
Therefore, SP = 120/100 * 1000 = Rs. 1200
Gain = 1200 – 850 = 350
Hence Gain % = 350/850 * 100 = 41.17%

Question 7: A man bought two bicycles for Rs. 2500 each. If he sells one at a profit of 5%, then how much should he sell the other so that he makes a profit of 20% on the whole?
Solution:
Before we start, it’s important to note here that it is not 15% to be added to 5% to make it a total of 20%.
Let the other profit percent be x.
Then, our equation looks like this.
105/100 * 2500 + [(100+x)/100] * 2500 = 120/100 * 5000 → x= 35.
Hence, if he makes a profit of 35% on the second, it comes to a total of 20% profit on the whole.

Question 8: A shopkeeper allows a discount of 10% on the marked price and still gains 17% on the whole. Find at what percent above the cost price did he mark his goods.
Solution:
Let the cost price be 100. Then SP = 117.
Let the marked price be x.
So, 90% of x = 117 → x = 130.
Therefore, he marked his goods 30% above the cost price.

 Question 9: A shopkeeper offers a discount of 20% on the selling price. On a special sale day, he offers an extra 25% off coupon after the first discount. If the article was sold for Rs. 3600, find

1. The marked price of the article and
2. The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.

Solution:
Let the marked price of the article be x.
First a 20% discount was offered, on which another 25% discount was offered.
So, 75% of 80% of x = 3600
75/100 * 80/100 * x = 3600 → x = 6000.
So the article was marked at Rs. 6000.
Cost price of the article = [100/(100+80)]*3600 = Rs. 2000.
It is important to note here that this DOES NOT equal to a 45% discount on the whole. When different discounts are applied successively, they CANNOT be added.

Question 10: By selling 5 articles for INR 15, a man makes a profit of 20%. Find his gain or loss percentage if he sells 8 articles for INR 18.4?
Solution: Questions of this type normally appear as part of a more complex problem in an exam like the GMAT.
Remember, such a question should be solved by you as soon as you finish reading the question by solving-while reading process, as follows.
By selling 5 articles for INR 15, a man makes a profit of 20% – SP = 3.
Hence, CP = 2.5, if he sells 8 articles for INR 18.4 – SP = 2.3.
Hence percentage loss = 8%.

Question 11: RFO Tripathi bought some oranges in Nagpur for 32 Rupees. He has to sell it off in Yeotmal. He is able to sell off all the oranges in Yeotmal and on reflection finds that he has made a profit equal to the cost price of 40 oranges. How many oranges did RFO Tripathi buy?
Solution:  Suppose we take the number of oranges bought as x. Then, the cost price per orange would be Rupees 32/x, and his profit would be
40 x 32/x = 1280/x.
To solve for x, we need to equate this value with some value on the other side of the equation. But, we have no information provided here to find out the value of the variable x. Hence, we cannot solve this

Question 12: A dishonest businessman professes to sell his articles at cost price but he uses false weights with which he cheats by 10% while buying and by 10% while selling. Find his percentage profit.
Solution: Assume that the businessman buys and sells 1 kg of items. While buying the cheats by 10%, which means that when he buys 1 kg he actually takes 1100 grams. Similarly, he cheats by 10% while selling that is, he gives only 900 grams when he sells a kilogram. Also, it must be understood that since he purportedly buys and sells the same amount of goods and he is trading at the same price while buying and selling, money is already equated in this case.
Hence, we can directly use:
% Profit = (Goods left x 100/Goods sold)
= 200 x 100/900 = 22.22%
Note that you should not need to do this calculation since this value comes from the fraction to percentage conversion table.
If you are looking at a 680+ plus score in quantitative ability you should be able to come to this solution under 90 seconds inclusive of problem reading time. And the calculation should go like this:
Money is equated – % profit = 2/9 = 22.22%