Quant (Concepts): Discounts and Profit

Quant (Concepts): Discounts and Profit

What does Store XYZ Gain, Marking P% and then Discounting P%

In the first go, it seems that the shopkeeper neither gains nor loses as he has increased the price by P% and then decreased it by P%. But this is quite misleading.

Marked Price:

In most shops, every article is marked or tagged with a card and its price is printed on it. This is called the Marked Price of that article, abbreviated as MP. This is also called as List price or Tag Price or Advertised Price.

It is the price at which a shopkeeper wishes to sell his goods. It can also be expressed as a certain percentage above the cost price of the article.

e.g. “A camera costing Rs. 7000 is marked up by 30%".

This means that:
CP = Rs. 7000 and MP = CP + 30% of CP
⇒ CP = Rs. 7000 + 2100
= Rs. 9100.

Discount:

In order to increase sales or clear old stock, shopkeepers offer rebate on the marked price. This rebate is known as Discount, usually expressed as a percentage.

e.g. “A camera costing Rs. 7000 is marked up by 30% and then, 30% discount is given“.

As calculated above:
MP = Rs. 9100.
Now, 30% discount is given on MP.
So, the discount given will be 9100 × 30/100
= Rs. 2730.

Selling price = (Marked price) - (Discount)
= Rs. 6370. 

Here, there is a loss as Selling price is less than the Cost price.

• Loss = Rs. 7000 – Rs. 6370 = Rs. 630.
• Loss % = 100 × Loss/Cost price = 9%.

There will always be loss in this case, where the increased percentage and decreased percentage is same.

Note: It can be concluded that it is a question of two successive changes, i.e. of X% increase followed by X% decrease. The first change was on CP and the second one was on MP.

Hence, the answer will be incorrect.

The direct formula is:

If the mark up is x% and discount is y%.
The Net % profit / loss = x – y – xy /100%.

Example1:

A trader marks his goods at 50% above the cost price and allows a discount of 25% during clearance sale. What is his gain percent?

Solution:

Net profit % = 50 – 25 - 50×25/100 = 12.5%.

Alternatively, Let the CP be Rs. 100.
Then, MP = Rs. 150.
Discount = 25% of Marked Price = Rs. 37.5

Selling Price = (Marked Price) - (Discount)
= 150 - 37.5 = 112.5

Gain % = (112.5 - 100)% = 12.5%

Example 2:

How much above the cost price should a shopkeeper mark his goods in percentage, so that after allowing a discount of 25% on the marked price, he still gains 20%?

Solution:

Let the cost price be Rs. 100.
Profit = 20%.
Therefore, selling price = Rs. 120.
Discount = 25% of MP

Selling Price = (Marked Price) - (Discount)
= MP – 0.25 MP = 0.75 MP

Therefore, 120 = 0.75 MP,
MP = 120 × 100/75 = 160.

Hence, the marked price is 60% above cost price.
Hence, the price marked should be 60% above the cost price.

Example 3:

How much does a shopkeeper gain/lose (in Rs.) allowing a discount of 40% on a washing machine, which he has marked up by 40% over his cost price of Rs 12000?

Solution:

Here, the cost price = Rs. 12000.
As discussed earlier, in this case there is always a loss.
Loss % = 40² /100 = 16%.
Loss is Rs. = 16% of CP = 12000 × 16/100
= Rs. 1920.

Example 4:

A DVD costing Rs. 500 is marked to be sold at a price, which gives a profit of 40%. What will be its selling price in a sale when 20% is taken off the marked price?

Solution:

As discussed earlier,
Net % change on CP = 40-20 - 40×20/100 = +12%
Profit in Rs. = 12% of CP = 500 × 12/100 = Rs. 60.

Hence SP = CP + Profit = Rs. 560.