In "Seconds" sale a shoe store all items are sold at an additional discount of 10% over amd above the usual discount for all items @ 10% on the marked price. A customer pays rupees 1620 for a particular pair of shoes. Find the marked price.
Answers
Answer:
In the first part of Profit and Loss series, we learnt the basic definitions and the meaning of Cost Price, Selling Price, Marked price etc. Let us revise the definition of Marked Price. As we saw earlier, traders are in the habit of marking their articles at a certain price above their costs. Then the discounts they offer are on this marked price, thereby they actually make sure that have already factored in the profit they want.

Discounts are offered on the marked price and the selling price is determined by the discount offered on the marked price. For the process of simplification, let us assume:
C = Cost price
S = Selling price
M = Market price
D% = Discount
G% = Gain
Now,
Discount = D% of marked price, M
Discount = Marked Price – Selling Price
Marked Price – Amount of Discount = Selling Price
M (1-D%) = Selling Price
Also, Selling Price = Cost Price + Gain
Thus,
M (1-D%) = C (1 + G%)
Or in other words
Marked Price (1 – Discount%) = Cost Price (1 + Gain%)
Example-1: Natasha offers her customers a discount of 10% on her beauty products and she still makes a profit of 20%. What is the actual cost to her of that beauty product marked Rs. 400?
Solution:
Marked price = Rs. 400
Discount = 10%
Profit = 20%
Therefore, the Selling Price = 90% of 400
Therefore 400 x 90/100 = Rs. 360
Selling price = Rs. 360
Profit = 20%
Cost price = 100/120 x 360 = Rs. 300
Profit and Loss: Concept of successive discounts
If successive discounts of x% and y% are allowed on the marked price M of the discount, then, after discount the customer finally ends up paying:
Selling Price = (1-x%)(1-y%) x Marked Price
If you look at the above formula closely, you would see that the multiplication is nothing else but a percentage equivalent of two successive percentage change on a number.
Example-2: Pankaj offers a 10% discounts on his goods and he offers a further discount of 5% on the reduced price to those customers who pay cash. What does a customer have to pay in cash for a cricket bat of Rs. 200?
Solution:
Price of the cricket bat = Rs. 200
After Discount of 10% Marked price would be Rs. 180
Since he is purchasing the bat by cash, so a discount of 5% is applicable again on the reduced marked price. Thus, the final selling price the cricket bat would be of Rs. 171
Profit and Loss: Basic Question types
Type-1: Comparing quantities of goods and prices
In these types of questions, CP of a fixed number of goods are compared with the SP of another field number of goods. Let us see through an example:
Example-3: The cost price of 30 articles is equal to the selling price of 40 articles. What is the profit or loss percentage?
Solution:
To obtain the same amount of money, which was needed to purchase 30 articles, we need to sell 40 articles, which is more than what we have got for the same sum. It means we need to arrange 10 more articles apart from the articles which we have purchased. So, there will be a loss.
Now, CP of 30 articles = SP of 40 articles Or, CP/SP = 30/40 =3/4
Or, 1 – CP/SP = 1- 3/4 = 1/4
So, Loss percentage
= (l – CP/SP) x 100 = 1/4x 100 = 25%
Alternatively,
CP of 30 articles = SP of 40 articles = Rs 120 (Assume) So, CP of one article = Rs 4 ,SP of one article = Rs 3 Obviously, there is a loss of Re 1 Loss percentage = 1,4 X 100 = 25%