In the profit and loss section, the cost of a product is very crucial. If you have marked the cost of the product wrong, you may not see any profit at all. In the following section, we will see what we mean by marked price. We will also see all the other relevant terms and try and understand how to determine marked price such that the profit is maximum. Let us begin with the following space below!

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## Marked Price

The price on the label of an article/product is called the marked price or list price. This is the price at which product is intended to be sold. However, there can be some discount given on this price and the actual selling price of the product may be less than the marked price. It is generally denoted by MP.

When Discount is offered, M.P. > S.P.

When Discount is not offered, M.P. < S.P.

Sometimes marked price is used as a psychological tool for customers. For example, a set of headphones is being sold at Rs 999/-. One company has set the marked price at Rs 1000/- thus showing a little discount on the marked price. Another company sells the same product at the same cost but marks it at Rs. 1499/- thus giving the illusion of a heavy discount. The customers are more likely to buy the one marked at a higher price. This brings us up to the concept of discount.

**Browse more Topics under Profit And Loss**

- Cost Price
- Fixed, Variable and Semi-variable Cost
- Selling Price
- List Price
- Margin
- Dishonest Dealers and Faulty Weights
- Percentage Loss
- Percentage Gain
- Discounts and Marked Price
- Equivalent Discount
- Equation-Based Questions
- Goods Passing Through Successive Hands
- True Discount
- Bankers Discount
- Profit and Loss Practice Questions

## Discount

Discount is defined as the amount of rebate given on the label price (marked price) of an article. It is given by merchants/shopkeepers for attracting customers for increasing their sales.

Discount = Marked Price – Selling Price

Discount percentage = [(Discount)/(Marked price)]× 100. Before going on to solve more examples, let us recall all the formulas that we have seen thus far.

### Main Concepts and Results

Discount is a reduction given on marked price.

- Discount = Marked Price – Sale Price (S.P.)

Discount can be calculated when a discount percentage is given.

- Discount = Discount % of Marked Price

Additional expenses made after buying an article are included in the cost price and are known as overhead expenses.

- cost price = buying price + overhead expenses

Sales Tax is charged on the sale of an item by the government and is added to the Bill Amount.

- Sales tax = Tax% of sale amount.
- These days, however, the selling prices (known as MRP) include the tax known as VAT (Value Added Tax).

The interest compounded annually is the interest calculated on the previous year’s amount A, (A = P + I).

The time period after which the interest is added each time to form a new principal is called the conversion period.

When the interest is compounded half-yearly, there are two conversion periods in a year of duration 6 months each.

## Solved Examples For You

Example 1: Namitha offers a discount of 20% on all the items at her shop and still makes a profit of 12%. What is the cost price of an article marked at Rs 280?

A) Rs. 160 B) Rs 180 C) Rs 200 D) Rs 240

Answer: We have the Marked Price = Rs 280. Also we have the Discount = 20% of Rs 280.

Thus we can write it as = (20/100) × 280 = Rs 56. So the selling price = Rs (280 – 56) = Rs 224.

Let the cost price be Rs 100. Profit = 12% of Rs 100 which is = Rs 12.

So selling price = Rs (100 + 12) = Rs 112. Now let us see further:

If the selling price is Rs 112, cost price = Rs 100. If the selling price is Rs 224, cost price = Rs (100/224) × 112 which is = Rs 200. Hence the answer is C) Rs 200.

Example 2: A bicycle marked at Rs 1,500 is sold for Rs 1,350. What is the percentage of the discount?

A) 8% B) 10% C) 12% D) 14.3%

Answer: Given : Marked Price = Rs 1500, and Selling Price = Rs 1350.

Amount of discount is = Marked Price – Selling Price. In other words we can say that = (1500 – 1350) = Rs 150.

Discount for Rs. 1500 =Rs 150

Therefore, the Discount for Rs 100 = (150/1500) × 100 = 10%

Thus, the Percentage of discount = 10% and the correct option is B) 10%.

Example 3: An almirah is sold at Rs 5,225 after allowing a discount of 5%. Find its marked price.

A) Rs. 3500 B) Rs. 4300 C) Rs. 5000 D) Rs. 5,500

Answer: Let us solve this using the following method:

The discount is given in percentage. Hence, the M.P. is taken as Rs 100. Rate of discount = 5%.

Amount of discount = (5/100)×100 = Rs 5.

Selling Price = M.P. – Discount = 100 – 5 = Rs. 95. If S.P. is Rs 95, then M.P. is Rs. 100. When S.P. is Rs. 5225, M.P. = Rs. (100/95) × 5225. Therefore the M.P. of the almirah = Rs. 5,500 and hence the correct option is D) Rs. 5,500.

Second Method: We can also use the following method. This is the easier and the faster way.

S.P. = Rs 5225 and Discount = 5%. Also, M.P. =?. Now we have:

M.P. = [100/(100 – Discount%)] × S.P. = [100/(100 – 5)] × 5225

In other words we may also write: Rs. (100/95) × 5225 = Rs. 5,500.

Example 4: A shopkeeper allows a discount of 10% to his customers and still gains 20%. Find the marked price of an article which costs Rs 450 to the shopkeeper.

A) Rs. 800 B) Rs 400 C) Rs 600 D) Rs 379

Answer: Let us use the formula method first:

Discount = 10%, Gain = 20%, C.P. = Rs. 450, M.P. = ?

M.P. = [(100 + Gain%)/(100 – Discount%)] × C.P.

Thus we have = [(100 + 20)/(100 – 10)]×450 = Rs. 600 and hence the correct answer is C) Rs 600.

## Practice Questions:

Q 1: Marked price of a table is Rs 1200. It is sold at Rs. 1056 after allowing a certain discount. Find the discount percentage?

A) 10% B) 12% C) 14% D) 16%

Ans: B) 12%

Q 2: What will be a single equivalent discount for successive discounts of 10% and 5% on the marked price of an article?

A) 14.5% B) 15.3% C) 16.01% D) 21%

Ans: A) 14.5%

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