How to Solve Profit, Loss, and Discount Questions?

Every company and business you see works on the concept of profit and loss. The concept of profit and loss is fundamental not only to running a business or company but also to keeping an account of your own expenditures.

The study of profit, loss, and discount makes business easy and are very practical concepts to learn and practise on a daily basis. It will help kids become smarter and gain knowledge, which is more important than merely academic knowledge.

Profit, Loss, and Discount

Terms Related to Profit and Loss

The term 'Profit and Loss' is a practical concept that helps to tackle real-life problems. The price marked on any good is 'Market Price'. When a shopkeeper sells a product, it is the 'selling price'. The price at which a shopkeeper purchases a product is its 'cost price'. When the shopkeeper sells the product at a greater price than its cost price, he gains a profit. If he sells it at a lesser price than C.P., then there is a loss.

So let us learn these terms in detail.

• Cost Price (C.P.) - The amount at which a product is purchased is its Cost Price (C.P.). Sometimes it also includes transportation charges and overhead expenses.

• Selling Price (S.P.) – The amount at which the product is sold is called its selling price (S.P.). It can be equal to the cost price or less than the C.P. or even more than the C.P. of the product.

• Profit (P) - If a product or good is sold at a price greater than its cost price, then we say that the seller made a profit out of it.

• Loss (L) - If a product is sold at a price less than its cost price, then we say that the dealer makes a loss.

• Profile Percentage (%P) - It is defined as the percentage of profit on the cost price. Whether it is the percentage of profit or loss we calculate it on the cost price.

$\text { %profit }=\dfrac{\text { profit }}{\text { Cost Price }} \times 100$

• Loss Percentage (%L) - It is the percentage of loss on the cost price.

$\% \text { Loss }=\dfrac{\text { Loss }}{\text { Cost Price }} \times 100$

What are Overhead Expenses, Market Price, and Discount?

• Overhead Expenses - Additional expenses on transportation, rent, repair, advertising, etc. are included in the original cost price of the product, i.e.,

Cost Price = Original Price + Overhead expenses

• Market Price - The printed price of an article or good is called a Market Price(MP).

• Discount - To motivate the buyers to buy products, stores offer sales of goods and discounts to the customer.

Concept of Profit and Loss with Examples

Let us understand the concept of profit and loss Maths questions with the help of an example. If a shopkeeper buys a pen at Rs. 10 and sells it at Rs. 20. We can say that the C.P. of the pen is Rs. 10. The amount at which he sells the pen is its S.P., i.e., Rs. 20. Now, here the selling price of a pen is more than its cost price. So, the shopkeeper gained profit.

$\text { C.P }=\mathrm{Rs} 10$

$\mathrm{~S} . \mathrm{P}=\mathrm{Rs} 20$

$\text { Profit }=\text { Selling Price }-\text { cost price }$

$=\mathrm{Rs} 20-R s 10$

$=\mathrm{Rs} 10$

Hence, the shopkeeper made a profit of $\mathrm{Rs} 10$

Now let us find the percentage of profit,

$ \% \text { Profit }=\dfrac{\text { profit }}{C P} \times 100$

$=\dfrac{10}{10} \times 100$

$=100 \%$

Therefore, the percentage profit becomes 100%.

Rules and Formulae

1. If the cost price is less than the selling price, then there is a profit.

i.e. C.P.<S.P. ~Profit

2. If the cost price is more than the selling price, there is a loss.

C.P.>S.P. ~ Loss

3. Profit = S.P. - C.P.

4. Loss = C.P. - S.P.

5. In order to find %profit or %loss,

$\text { %profit }=\dfrac{\text { profit }}{\text { CostPrice }} \times 100$

$\% \text { Loss }=\dfrac{\text { Loss }}{\text { CostPrice }} \times 100$

6. Discount = Marked Price - Selling Price

7. %Discount = Discount/Marked Price × 100

8. S.P. = M.P. - Discount

9. M.P. = S.P. + Discount

10. If Profit is made then, C.P. = M.P. - (Discount + Profit)

11. If Loss is made then, C.P. = M.P. - (Discount - Loss)

Solved Examples

Given below are solved profit and loss Maths questions along with the discount questions.

1. Find the selling price of the bicycle of Rs. 1000 if

(a) Loss is Rs. 50.

Ans: Here, C.P. of bicycle = Rs. 1000

Loss (L) = Rs. 50

We know that in case of loss, C.P.>S.P.

Therefore, the formula of loss is

Loss = C.P. - S.P.

Let S.P. be 'Rs. x'

Therefore, 50 = 1000 - x

x = 1000 - 50

= Rs. 950

S.P. of a bicycle = Rs. 950

Now, C.P. = Rs. 1000

(b) If %Profit is 50%.

Ans: Let profit be ' $x^{\prime}$

$\% \mathrm{P}=50$

By formula of %profit,

$\text { %profit }=\dfrac{\text { profit }}{\text { CostPrice }} \times 100$

$50=\dfrac{x}{1000} \times 100$

$x= 10 \times 50$

$=Rs 500$

Hence, the profit is Rs. 500.

Now, S.P. = C.P. $+P$

$=1000 + 500 = 1500$

The selling price of a bicycle is Rs. 1500.

2. A student bought a bag for Rs. 350 and later sold it for Rs. 400. Find the profit percentage he earned.

Ans: Here, CP = 350, and SP = 400

As SP>CP,

So, Profit = SP – CP

Profit = 400 – 350 = 50.

Profit% = $\dfrac{50}{350} \times 100$

Profit%=$\dfrac{100}{7}$

So, profit% is $\dfrac{100}{7}$

3. If the list price of a book is $50$, and a $10$ discount is offered on the book, then what is the discount percentage?

Ans: Discount % = (Discount/marked Price) × 100

Marked Price = $50; discount = $10

Discount (%) = $\dfrac{10}{50} \times 100$

= $\dfrac{100}{5}$

= 20%

Therefore, the discount percentage is calculated as 20%.

Practice Questions

Here, we will have a profit-and-loss practice set.

1. If C.P. = Rs. 10,500, S.P. = 11,500, then find out the profit.

Ans: Rs. 1000

2. Raju buys a scooter for Rs. 4,700 and spends Rs. 800 on its air. If the selling price of a scooter is Rs. 5800, then what is his % gain?

Ans: $\dfrac{60}{11}$ %

3. If the S.P. of 16 items is the same as the C.P. of 20 items, then what is the %gain?

Ans: A gain of 25%

Summary

We have learned how to find profit, loss, and discount in detail. There are also some profit and loss Maths questions to understand the core of the complete topic. Students will also master the concept with profit and loss practice sheets. As we have learned, the formula $\text { %profit }=\dfrac{\text { profit }}{\text { Cost~Price }} \times 100$. Later on $\% \text { Loss }=\dfrac{\text { Loss }}{\text { Cost Price }} \times 100$. Students can also master the concept by solving profit and loss MCQ. The concept of profit and loss will help them deal better in the market and boost their confidence. It will help them in their practical life, rather than just clear theory.