Profit And Loss Questions – Solve Profit And Loss Problems

If you are looking for practice questions and tricks to master Profit and Loss topic, you have come to the right place. We have provided some commonly asked questions related to profit and loss concepts in the exam along with formulas, concepts, and tricks to save you some time in exams. The Profit and Loss Questions provided here are curated to revise your concepts and make you confident on solving gain and loss questions. To check how much you are confident on the profit & loss topic, we have provided some practice questions for you to practice along with solved examples.

Profit And Loss Questions: Solved Examples On Profit & Loss

Here are some of the solved questions on profit and loss concept:

Q1: Alfred buys an old scooter for Rs. 4700 and spends Rs. 800 on its repairs. If he sells the scooter for Rs. 5800, find his gain percent:
A: Cost Price (C.P.) = Rs. (4700 + 800) = Rs. 5500.
Selling Price (S.P.) = Rs. 5800.
Gain = (S.P.) – (C.P.) = Rs. (5800 – 5500) = Rs. 300.
Gain %
$$ = \left( {{{300} \over {5500}} \times 100} \right)\% = 5{5 \over {11}}\% $$

Q2: The percentage profit earned by selling an article for Rs. 1920 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
A: Let C.P. be Rs. x.
$${{1920 – x} \over x} \times 100 = {{x – 1280} \over x} \times 100$$
⇒ 1920 – x = x – 1280
⇒ 2x = 3200
⇒ x = 1600
Required SP = 125% of Rs. 1600
$$ = Rs.\,\left( {{{125} \over {100}} \times 1600} \right) = Rs.\,2000$$

Q3: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
A: SP = 85% of Rs. 1400
$$ = Rs.\,\left( {{{85} \over {100}} \times 1400} \right) = Rs.\,1190$$

Q4: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
A: Cost Price of 1 toy
$$ = Rs.\,\left( {{{375} \over {12}}} \right) = Rs.\,31.25$$
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 – 31.25) = Rs. 1.75
$$ ∴ Profit\,\% = \left( {{{1.75} \over {31.25}} \times 100} \right)\% = {{28} \over 5}\% = 5.6\% $$

Q5: Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. What is the gain percent?
A: Suppose, number of articles bought = L.C.M. of 6 and 5 = 30
C.P. of 30 articles
$$= Rs.\,\left( {{5 \over 6} \times 30} \right) = Rs.\,25$$
S.P. of 30 articles
$$= Rs.\,\left( {{6 \over 5} \times 30} \right) = Rs.\,36$$
$$ ∴ Gain\,\% = \left( {{{11} \over {25}} \times 100} \right)\% = 44\% $$

Q6: A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 392, what was his profit?
A: $$CP = Rs.\,\left( {{{100} \over {122.5}} \times 392} \right) = Rs.\,\left( {{{1000} \over {1225}} \times 392} \right) = Rs.\,320$$
∴ Profit = Rs. (392 – 320) = Rs. 72.

Q7: On selling 17 balls at Rs. 720, there is a loss equal to the cost price of 5 balls. The cost price of a ball is:
A: (C.P. of 17 balls) – (S.P. of 17 balls) = (C.P. of 5 balls)
⇒ C.P. of 12 balls = S.P. of 17 balls = Rs.720.
⇒ C.P. of 1 ball
$$Rs.\,\left( {{{720} \over {12}}} \right) = Rs.\,60$$

Q8: When a plot is sold for Rs. 18,700, the owner loses 15%. At what price must that plot be sold in order to gain 15%?
A: 85 : 18700 = 115 : x
$$ \Rightarrow \,x = \left( {{{18700 \times 115} \over {85}}} \right) = 25300$$
Hence, SP = Rs. 25300.

Q9: The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
A: Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 – x).
$$ ∴ \left( {{{20 – x} \over x} \times 100 = 25} \right)$$
⇒ 2000 – 100x = 25x
⇒ 125x = 2000
⇒ x = 16.

Q10: If selling price is doubled, the profit triples. Find the profit percent.
A: Let C.P. be Rs. x and S.P. be Rs. y.
Then, 3(y – x) = (2y – x)
⇒ y = 2x.
∴ Profit = Rs. (y – x) = Rs. (2x – x)
= Rs. x
$$Profit\,\% = \left( {{x \over x} \times 100} \right)\% = 100\% $$

Q11: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
A: Let C.P.= Rs. 100. Then, Profit = Rs. 320, S.P. = Rs. 420.
New C.P. = 125% of Rs. 100 = Rs. 125
New S.P. = Rs. 420.
Profit = Rs. (420 – 125) = Rs. 295.
$$Required\,percentage = \left( {{{295} \over {420}} \times 100} \right)\% = {{1475} \over {21}}\% = 70\% \,(approximately)$$

Q12: A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%?
A: C.P. of 6 toffees = Re. 1
S.P. of 6 toffees = 120% of Re. 1 = Rs. 6/5
For Rs. 6/5, toffees sold = 6
For Re. 1, toffees sold
$$\left( {6 \times {5 \over 6}} \right) = 5$$

Q13: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
A: S.P. = 85% of Rs. 1400
$$ = Rs.\,\left( {{{85} \over {100}} \times 1400} \right) = Rs.\,1190$$

Q14: 100 oranges are bought at the rate of Rs. 350 and sold at the rate of Rs. 48 per dozen. The percentage of profit or loss is:
A: C.P. of 1 orange
$$ = Rs.\,\left( {{{350} \over {100}}} \right) = Rs.\,3.50$$
S.P. of 1 orange
$$ = Rs.\,\left( {{{48} \over {12}}} \right) = Rs.\,4$$
$$∴ Gain\,\% = \left( {{{0.50} \over {3.50}} \times 100} \right)\% = {{100} \over 7}\% = 14{2 \over 7}\% $$

Q15: A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. What is his total gain or loss percent?
A: C.P. of 1^st transistor
$$Rs.\,\left( {{{100} \over {120}} \times 840} \right) = Rs.\,700$$
C.P. of 2^nd transistor
$$Rs.\,\left( {{{100} \over {96}} \times 960} \right) = Rs.\,1000$$
So, total C.P. = Rs. (700 + 1000) = Rs. 1700
Total S.P. = Rs. (840 + 960) = Rs. 1800
$$Gain\,\% = \left( {{{100} \over {1700}} \times 100} \right)\% = 5{{15} \over {17}}\% $$

Problems On Profit And Loss

Here are some of the practice questions on profit and loss concepts for you to practice:

Q1: A real estate agent sells two sites for Rs. 18000 each. On one he gains 25% and on the other, he loses 25 %. What is his loss or gain percent?

Q2: If a retailer marks up his price by 30 % and then allows a 30 % discount, what is his percentage profit or loss?

Q3: By selling an article for Rs 600 more, Karthik would have made 5% profit on his sale instead of an 11% loss. What was his cost price?

Q4: I make a profit of 20% by selling an article. What would be the profit percent if it were calculated on the selling price instead of the cost price?

Q5: A tradesman marks his goods 25% above the cost price and allows his customers 12 % reduction on their bills. What percent profit does he make?

Q6: In order to maintain the price line, a trader allows a discount of 12 % on the marked price of goods on his ship. However, he still makes a gross profit of 32 % on the cost price. Find the profit percent he would have made on the selling price had he sold at the marked price.

Q7: An orange vendor makes a profit of 10% by selling oranges at a certain price. If he charges Rs. 1.4 higher per orange he would gain 30%. Find the original price at which he sold an orange.

Q8: A man bought a horse for a certain sum and sold it, at a loss of 8 % on his outlay. If he had received Rs. 1800 more, he would have gained 14½ % on his outlay. What did the horse cost?

Q9: Divya made a profit of 25% when selling a Salwar Kameez at Rs. 4,000. Find the cost price of the same dress.

Q10: What profit percent is made by selling an article at a certain price if by selling at four-fifth of that price there may be a loss of 12 %?

Answers:

Profit And Loss Concepts

Let’s revise important concepts related to profit and loss (gain and loss):

⇒ Profit: The amount gained by selling a product at more than its cost price. It is the difference between the SP (selling price) and CP (cost price) of a product.

⇒ Loss: The amount lost due to selling a price at lower price than its cost price is the loss. It is the difference between CP (cost price) and SP (selling price) of an item.

⇒ Cost Price (CP): The amount paid for a product or commodity to purchase it is called its cost price. Cost price is further classified into two different categories:

1. Fixed Cost: The fixed cost is constant, it doesn’t vary under any circumstances.
2. Variable Cost: It could vary depending as per the number of units.

⇒ Selling Price (SP): The amount for which the product is sold is called its selling price. It is sometimes also called as sale price.

Let’s see the important profit and loss formulas which will help solve the questions.

Important Points To Remember

1. For-profit, the selling price should be more than the cost price
2. For loss, cost price should be more than the selling price.
3. The percentage value for profit and loss is calculated in terms of cost price.
4. Loss or gain is always reckoned on CP.

FAQs On Profit And Loss Questions

Some of the frequently asked questions on profit and loss are:

Now we have provided you with different types of profit and loss questions. We hope this detailed article is helpful to you. If you have any queries, ping us through the comment box below and we will get back to you as soon as possible.