If a seller gives a discount of 15% on retail price

Thank you Shameekv1989.

This is a simple question on the topic of Profit, Loss and Discount.

To work out this problem, let us remember that SP = CP (1+\(\frac{p}{100}\)) where ‘p’ represents the profit percentage. SP = MP(1-\(\frac{d}{100}\)) where MP represents the Marked Price (or also known as Retail price) and ‘d’ represents the discount percentage.

Let the MP be 100x. Then,

Amount of discount given = 15% of 100x = 15x. Therefore, SP = MP – Discount = 85x. This 85x represents 2% more than the cost price since there was a 2% profit.

That is, 85x = 102% of the CP. Therefore,

CP = \(\frac{85x * 100 }{ 102}\). Notice that 85 and 102 are both multiples of 17. This is an indicator that you will be able to cancel off these numbers and obtain a neat little number for CP which can be dealt further (rather than ending up with vulgar decimals); this should tell you that you are on the right track.

CP = \(\frac{500x }{ 6}\) or CP = \(\frac{250x }{ 3}\).

If she wants to make a profit of 20%, her selling price should be 120% of the CP. This means,

Intended selling price = \(\frac{6}{5}\) * \(\frac{250x }{ 3}\) = 100x. This is the MP (or the retail price) we assumed at the start. This means that she has to sell the article AT RETAIL PRICE to obtain a 20% profit.

The correct answer option is D.

Hope that helps!

Thank you Aravind,
Your explanation made it more clear to me.

chetan2u
after 15% discount, sp is 85, assuming sp was a 100

we find the cp using: (85-cp)/cp = 0.02 --> this gives us cp as an ugly fraction, which is 85/1.02.
lets ignore that ugly fraction and call it cp

to make a 20% profit

(sp-cp)/cp = 0.2
and solving for sp we get 1.2cp

this tells us that we have to sell at sp to make a 20% profit

which bring me to my question:

could we have just said that we need to sell at the retail price to make 20% profit? seeing how that ugly cp fraction is never used?

Create a table as under
Answer must be (D)

Let retail price be 100
100*(100-15/100) = 85
Ratio is sell at 85, get 102
85:102 = x:120

85/102 = x/120
x=100

100 is the same as retail price, so to make 20%, need to sell at retail price

let SP be 100
15% discount will be 85
still a profit of 2% is made i.e. retail price must have been 102
so as to make profit of 20% ; selling price has to be 85*1.2 ; 102

option D

Given; If a seller gives a discount of 15% on retail price, she still makes a profit of 2%.
Asked: Which of the following ensures that she makes a profit of 20%?

Let the retail price be x and cost price be y.

At 15% discount
(100%-15%)x = .85x = 1.02y

For 20% profit
(100%+20%)y = 1.2y = .85x/1.02*1.2 = x

To generate 20% profit, he should sell at retail price

IMO D