# Profit & Loss

DEFINITIONS:

SALES PRICE (SP): The price at which goods/services are sold

COST PRICE (SP): The expenses occurred in making a product (or providing a service) and it includes the price of the raw material.

REVENUE: is compensation received for your product or services.

COST OF GOODS SOLD: are the variable expenses related to the sale of your product.

OPERATING EXPENSES: are fixed expenses, such as rent, and utilities.

OPERATING INCOME: is profit after operating income.

EARNINGS BEFORE TAXES: is income including other income and expenses, but before taxes.

INCOME TAXES: are federal, state, and local taxes.

NET EARNINGS: is the profit earned by the business, and it includes all expenses, including taxes.

If the shop sells a thing for more than they paid for it, then the difference is the 'profit':

profit = selling price - cost price

If the shop sells a thing for less than they paid for it, then the difference is the 'loss':

loss = cost price - selling price

Both profit and loss can be expressed either in dollars, OR as a percentage of the cost price.

Profit Percentage = (Profit / Cost Price) * 100

Occasionally profit is also mentioned in terms of sales price i.e

Profit on selling price= (Profit / Sales Price) * 100

Several problem types based on these formulas are discussed in the examples below

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Q1. If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?

ANS: If the merchant offers a discount of 40% on the marked price, then the goods are sold at 60% of the marked price.

The question further states that when the discount offered is 40%, the merchant sells at cost price.

Therefore, selling @ 40% discount = 60% of marked price (M) = cost price (C)

i.e., a mark up 66.66%

Q2. A shopkeeper bought an almirah from a wholesale dealer for Rs 4500 and

sold it for Rs 6000. Find his profit or loss percent.

Answer: Here C.P. of the almirah = Rs 4500

S.P. of the almirah = Rs 6000

Since S.P. > C.P., there is a profit

Profit = S.P. – C.P.

= Rs 6000 – Rs 4500

= Rs 1500

Profit % = 1500/4500 = 33.33% .

Q3. A dealer marks his goods 10% above the cost price and allow 10% discount. What does he gain or loose percent?

Q4. A shopkeeper buys scientific calculators in bulk for $15 each. He sells them for $40 each.

Q5. A trader professes to sell his goods at a loss of 8% but weights 900 grams in place of a kg weight. Find his real loss or gain per cent ?

Answer: The trader professes to sell his goods at a loss of 8%. Therefore, Selling Price = (100 - 8)% of Cost Price

or SP = 0.92CP

But, when he uses weights that measure only 900 grams while he claims to measure 1 kg.

Hence, CP of 900gms = 0.90 * Original CP

So, he is selling goods worth 0.90CP at 0.92CP

Therefore, he makes a profit of 0.02 CP on his cost of 0.9 CP

profit %= 2.22%

Q6. Calculate the profit on each calculator in dollars, and as a percentage of the cost price.

Answer: Given cost price = $15, selling price = $40

profit = selling price - cost price

= $40 - $15

= $25

Expressing the profit as a percentage of the cost price:

$profit

profit% = ------------------------ × 100%

$cost price

$25

= -------- × 100% = 166.7%

$15

Q7. : A retailer buys a cooler for Rs 3800 and overhead expenses on it are

Rs 50. If he sells the cooler for Rs 4400, determine his profit percent.

Answer : Here, C.P. of the cooler = Rs (3800 + 50) = Rs 3850

S.P. of the cooler = Rs 4400

Since S.P. > C.P., there is a profit

Profit = Rs 4400 – Rs 3850

= Rs 550

Profit % = 14. 27%.

Q8. A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

Answer:

Let S be the selling price of 1 article.

Therefore, the selling price of 100 articles = 100 S. --(1)

The profit earned by selling these 100 articles = selling price of 75 articles = 75 S -- (2)

We know that Selling Price (S.P.) = Cost Price (C.P) + Profit -- (3)

Selling price of 100 articles = 100 S and Profit = 75 S from (1) and (2). Substituting this in eqn (3), we get

100 S = C.P + 75 S. Hence, C.P = 100 S - 75 S = 25 S.

Profit % = 300%

Q9.A purchased a car for Rs. 1,35,000/- and spent Rs. 25,000/- for repairs. At what cost the car was sold if he earned 10% profit on it?

Q10. A florist bought 360 roses at $10 per dozen. If he sold them at $1.10 each, what is his profit as a percentage of selling price?

Q11. A garrison has enough food to last for 24 days. How much longer will the food last if each individual ration have to be reduced if the food is to last 40 days?

Q12. A trader buys goods at a 19% discount on the label price. If he wants to make a profit of 20% after allowing a discount of 10%, by what % should his marked price be greater than the original label price?

Answer:Let the label price be = Rs.100. The trader buys at a discount of 19%.

Hence, his cost = 100 - 19 = 81.

He wants to make a profit of 20%. Hence his selling price = 1.2 (81) = 97.2

However, he wants to get this Rs.97.2 after providing for a discount of 10%. i.e. he will be selling at 90% of his marked price.

Hence, his marked price M = = 108 which is 8% more than the original label price.

Q13. The cost price of 40 articles is equal to the selling price of 35 articles. What is the profit /loss percent?

Answer :

Let the cost price of one article be $1, then the cost price of 40 articles is $40

The question states that the selling price of 35 articles = cost price of 40 articles = $40

Therefore, now we know the selling price for 35 articles

Now, let us find the cost price for 35 articles.

We have assumed the cost of 1 article = $1. Therefore, cost price of 35 articles = $35

Therefore, the profit/loss made on 35 articles = S.P of 35 articles - C.P of 35 articles

i.e., $40 - $35= $5, or a profit of $5

Hence, % Profit =

= = 14.28% profit

Q14. A machine is sold at a profit of 10%. Had it been sold for $40 less, a loss of 10% would have been incurred. What is the Cost Price of the machine?

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Q15. A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

Answer :

Let S be the selling price of 1 article.

Therefore, the selling price of 100 articles = 100 S. -- (1)

The profit earned by selling these 100 articles = selling price of 75 articles = 75 S -- (2)

We know that Selling Price (S.P.) = Cost Price (C.P) + Profit -- (3)

Selling price of 100 articles = 100 S and Profit = 75 S from (1) and (2). Substituting this in eqn (3), we get

100 S = C.P + 75 S. Hence, C.P = 100 S - 75 S = 25 S.

Profit % =

Q16. A merchant buys two articles for Rs.600. He sells one of them at a profit of 22% and the other at a loss of 8% and makes no profit or loss in the end. What is the selling price of the article that he sold at a loss?

Answer: 404.70

Q17. Rajiv sold an article for Rs.56 which cost him Rs.x. If he had gained x% on his outlay, what was his cost?

Answer:Rs. 40

Q18. If apples are bought at the rate of 30 for a rupee. How many apples must be sold for a rupee so as to gain 20%?

Answer:25

Q19. A mechanic purchased two motor bikes for $7,500 and $6,000 respectively. He sold the first one for a profit of 15% and the second bike for a loss of 20%. How much did he lose or gain on both the transactions together?

$60 loss

$75 loss

$75 profit

$80 profit

Q20. A school bookshop sells an outdated biology text book for $49.35, making a 6% loss.What was the cost price of the book, and what is the cash value of the loss?

Q21. Two merchants sell, each an article for Rs.1000. If Merchant A computes his profit on cost price, while Merchant B computes his profit on selling price, they end up making profits of 25% respectively. By how much is the profit made by Merchant B greater than that of Merchant A?

Answer: Rs. 50

Q22. A fruit vendor purchased four branches of bananas consisting of 540 fruits in all for $168.75. He sold 15 dozens at 2 bananas a dollar, another 15 dozens at 3 bananas a dollar and the remaining at 5 bananas a dollar. Find his loss or gain percentage.

10 2/9% loss

13 1/4% profit

10 2/9% profit

13 1/4% loss

Q23. By selling a scooter to a customer for Rs 22400 an auto-dealer makes a profit of 12%. Find the cost price of the scooter.

Q24.A merchant marks his goods up by 75% above his cost price. What is the maximum % discount that he can offer so that he ends up selling at no profit or loss?

Answer: 42.85%

Q25. By selling a cycle for Rs 2024, a cycle merchant loses 12%. If he wishes

to make a gain of 12%, what will be the selling price of the cycle ?

Q26. If the cost price of 15 articles is the same as the selling price of 12 articles, find the gain or loss percent in the transaction.

Q27.A trader purchased 5000 coconuts, at $110 per 100 coconuts. 10% of the coconuts were damaged during transportation. He spent $575 for the transportation. If he gained 40% profit, at what price did he sell them?

$3.15 each

$1.89 each

$1.50 each

$2.00 each

Q28. A merchant marks his goods up by 60% and then offers a discount on the marked price. If the final selling price after the discount results in the merchant making no profit or loss, what was the percentage discount offered by the merchant?

Q29. By selling 45 oranges for Rs 160, a women loses 20%. How many oranges

should she sell for Rs 112 to gain 20% on the whole ?

Q30. A sells an article costing Rs 1000 to B and earns a profit of 6%. B, in turn sells it to C at a loss of 5%. At what price did C purchase the article ?

Q31. By selling 90 ball pens for Rs 160, a person loses 20%. How many ball pens should he sell for Rs 96, so as to have a gain of 20% ?

Q32. If the selling price of 20 articles is equal to the cost price of 23 articles, find the loss or gain percent.

Q33.A watch was sold at a profit of 12%. Had it been sold for Rs 33 more, the profit would have been 14%. Find the cost price of the watch.

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