Profit and Loss - Key Formulas
Basic Profit and Loss Formulas
To calculate profit or loss:
Where:
S.P. = Selling Price
C.P. = Cost Price
Profit and Loss Percentage
To calculate profit or loss percentage:
Finding Cost Price
To find the cost price:
Finding Selling Price
To find the selling price:
False Weights Formula
When using false weights:
Where:
Error = True weight - False weight
Successive Discounts
For successive discounts a%, b%, c%:
Example: For 20% and 10% successive discounts:
Net Discount = 100 - [(80×90)/100] = 28%
Profit and Loss Problems
Practice aptitude questions on profit and loss calculations
Question 1:
A shopkeeper sells an article for Rs. 200 with a loss of Rs. 20 %. Find the cost price of the article.
Cost Price = [100 × S.P.] / (100 - Loss%)
We are given that,
S.P. = Rs. 200 and loss = 20%
Cost Price = [100 × 200] / (100 - 20)
Cost Price = [100 × 200] / 80
Cost Price = Rs. 250
Question 2:
A trader expects a gain of 15% on his cost price. If in a week his sale is of Rs. 580, then what is his profit?
Cost Price = [100 × S.P.] / (100 + Gain%)
Cost Price = [100 × 580] / (100 + 15)
Cost Price = [100 × 580] / 115 = Rs. 504.35
Therefore,
Profit = S.P. - C.P.
Profit = 580 - 504.35 = Rs. 75.65
The trader gets a profit of Rs. 75.65
Question 3:
If a boy sells a book for Rs. 450 he gets a loss of 10%, then find cost price. To gain 10%, what should be the selling price?
1) Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. - (10% of C.P.)
S.P. = x - (0.10x)
450 = 0.9x
x i.e cost price = Rs. 500
2) Find Selling Price to gain 10%.
Selling Price = [(100 + Gain%) × C.P.] / 100
Selling Price = [(100 + 10) × 500] / 100
Selling Price = [110 × 500] / 100
Therefore, selling Price = Rs. 550
Question 4:
A merchant sells 30 metres of cloth and gains selling price of 10 metres. Find the gain percent.
Here, selling price of 10 m cloth is obtained as profit.
Profit of 10 m cloth = (S.P. of 30 m cloth) - (C.P. of 30 m cloth)
Selling price of 20 m cloth = Selling Price of 30 m of cloth
Let cost of each metre be Rs. 100.
Therefore, cost price of 20 m cloth = Rs. 2000 and S.P. of 20 m cloth = Rs. 3000
Profit% = (10/20) × 100 = 50%
Profit of 50% was made by the merchant.
Question 5:
S.P. of 10 candles is same as C.P. of 12 candles. Find the gain percent.
When number of Y articles > Number of X articles:
Profit% = [(No. of Y articles - No. of X articles) / No. of X articles] × 100
No. of X articles = 10
No. of Y articles = 12
Therefore,
Profit% = [(12 - 10) / 10] × 100 = [2/10] × 100
Profit% = 20%
Question 6:
The selling price of 40 apples is equal to cost price of 35 apples. Find the profit or loss obtained.
Let C.P. of each apple be Re 1/-.
Therefore,
C.P. of 40 apples = Rs. 40
S.P. of 40 apples = Rs. 35
C.P. of 40 apples > S.P. of 40 apples
Loss = 40 - 35 = Rs. 5
Loss% = (Loss / C.P.) × 100
Loss% = (5/40) × 100 = 12.5%
Question 7:
A man purchased two plots for Rs. 5,00,000. On one he gains 15% while on the other he loses 15%. Find how much does he gain or lose in the transaction.
Generally in such cases, there is always loss.
When two materials are sold and if one material gets profit and the other gets a loss, then:
Loss% = [(Common loss and gain%)²/100]
Therefore, here common loss and gain% = 15%
Hence,
Loss% = (15²/100) = 2.25%
Question 8:
A boy bought camel and carriage for Rs. 5000. He sells the camel at a gain of 20% and the carriage at a loss of 10%. If he gains 3% on the whole, then find the cost of the camel.
Let cost price of camel be x.
As cost of camel and carriage = Rs 5000
Cost of carriage = Rs. (5000 - x)
After selling camel he gains 20% and on carriage a loss of 10%. But on the whole he gains 3%.
Therefore,
20% of x - 10% of (5000 - x) = 3% of 5000
(20/100) × x - (10/100) × (5000 - x) = (3/100) × 5000
(x/5) - [(5000 - x)/10] = 150
[10x - (5000 - x) × 10] / 50 = 150
[10x - 50000 + 10x] / 50 = 150
20x - 50000 = 7500
20x = 57500
x = 2875
The cost of camel = Rs. 2167
Question 9:
A man sells one camera A for Rs. 7500 at a gain of 20% and another camera B for Rs. 8550 at a loss of 5%. Find his total loss or gain%.
C.P. of camera A = [100 × 7500] / (100 + 20) = [100 × 7500] / 120 = Rs. 6250
C.P. of camera B = [100 × 8550] / (100 - 5) = [100 × 8550] / 95 = Rs. 9000
Total C.P. = Cost of camera A + Cost of camera B
Total C.P. = 6250 + 9000 = Rs. 15250
Total S.P. = 7500 + 8550 = Rs. 16050
Selling Price > Cost Price, hence man gains during this transaction.
Gain = S.P. - C.P. = 16050 - 15250 = Rs. 800
Gain% = (Gain / C.P.) × 100
Gain% = (800 / 15250) × 100 = 5.24% ≈ 5.2%
Question 10:
A shopkeeper sells his goods at cost price but uses a weight of 970 grams for a kg. weight. What is his gain percent?
Gain% = [Error / (True weight - Error)] × 100%
Error = True weight - False weight
Error = 1000 - 970 = 30
Gain% = [30 / (1000 - 30)] × 100%
Gain% = [30 / 970] × 100% = 3.09%
Question 11:
A dishonest shopkeeper sells his grocery using weights 10% less than true weights and makes a profit of 30%. Find his total gain percentage.
Let weight of grocery bag be 1000 gm.
Now, the shopkeeper sells his grocery using weights 10% less than true weights.
Hence, actual weight of bag = 90% of 1000 gm = 900 gm
If each gram = Re.1, C.P. of each bag containing 900 gm = Rs. 900
The shopkeeper sells with a gain of 30% on true C.P.
Calculate the S.P.
Selling Price = [(100 + Gain%) × C.P.] / 100
Therefore,
Selling Price = [130 × 1000] / 100 = Rs. 1300
Gain = S.P. - C.P. = 1300 - 900 = Rs. 400
Gain% = (Gain / C.P.) × 100
Gain% = (400 / 900) × 100 = 44.44%
Question 12:
A dealer sells his goods at cost price. If by using false weights he gains 4 8/23%, then find the weight he uses for 1 kg.
Gain% = [Error / (True weight - Error)] × 100%
We are given that, dealer gains 4 8/23% after selling the goods at cost price.
Let error be x.
4 8/23% = [x / (1000 - x)] × 100%
100/23 = [100x / (1000 - x)]
(1000 - x) = 23x
1000 = 24x
x = 41.66
False weight = True weight - Error
False weight = 1000 - 41.66 = 958.34 gms
The false weight used by the dealer is 958.34 grams.
Question 13:
After two successive discounts, a tie with a list price of Rs. 120 is available at Rs. 90. If second discount is 9%, what is the first discount?
Let first discount = x
91% discount of (100 - x)% of 120 = 90
91/100 × (100 - x)/100 × 120 = 90
(100 - x) = (90 × 100 × 100) / (120 × 91) = 82.42
x = (100 - 82.42) = 17.58
Therefore, first discount = 17.58%
Question 14:
Find the single discount equivalent to a series discount of 30%, 20% and 10%.
Let marked price be Rs. 100
Therefore, selling price = 90%, 80% and 70% of Rs. 100
Selling Price = (90/100) × (80/100) × (70/100) × 100 = 50.4
Selling Price = Rs. 50.4
Required discount = Marked Price - Selling Price
= 100 - 50.4
= 49.6%
Question 15:
A dealer marks price of all the goods at 30% above the cost price and assumes that he will make a profit of 15% if he offers a discount of 15%. Find what will be his actual profit on sales?
Let cost price goods be Rs. 100
Marked price (Selling Price) marked by the shopkeeper on goods = Rs. 130
He sells the goods at a discount of 15%
Therefore,
Selling price = 85% of Rs. 130 = Rs. 110.50
Gain = S.P. - C.P. = 110.5 - 100 = 10.50%
Alternate solution:
He sells the goods at a discount of 15%
15% discount on Rs. 130 = Rs. 19.50
Selling Price = Marked Price - Discount = 130 - 19.50 = Rs. 110.50
Gain = S.P. - C.P. = 110.5 - 100 = 10.50%
Question 16:
A manufacturer sells a pair shoes to a wholesale dealer at a profit of 20%. Wholesaler sells them to retailer at a profit of 25%. The shoes are again sold to the customer for Rs. 50.50, thereby earning a profit of 30%. Find the cost price of manufacturer.
Profit earned by manufacturer = 20%
Profit earned by wholesaler = 25%
Profit earned by retailer = 30%
S.P. of shoes = Rs. 50.50
Therefore, 130% of 125% of 120% of x = 50.50
= (120/100) × (125/100) × (130/100) × x = 50.50/100
(195/100) × x = 50.50/100
x = (50.50 × 100) / (195)
x = 25.89
Cost price of shoes = Rs. 25.89