Profit and Loss | Definitions, Formulas, Solved Problems:
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 market 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.
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%.
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?
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.
Cost price of 10 toys = Rs. 40 → CP of 1 toy = Rs. 4.
The 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?
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.
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?
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.
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 The marked price of the article and
The cost price if the shopkeeper still makes a profit of 80% on the whole after all discounts are applied.
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.
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