Profit and Loss  Atreya Roy

Author: Atreya Roy is pursuing his BTech From Kalyani Government Engineering College, Bengal.
We buy different items from the market, and they have definite cost prices, selling prices, we may sometimes get discounts or free items. In this chapter we will learn them all, but before that we must have knowledge about a few things :
 Cost Price : It is the price at which the article is bought.
 Selling Price: It is the price at which the article is sold.
 Profit: If Selling Price is more than Cost Price, there is a GAIN
 Loss: If Cost Price is more than Selling Price, there is a LOSS
Cost Price and Selling Price are also denoted by CP and SP respectively.
So mathematically:
Profit= SP – CP
Loss = CP SP
Also, Profit / Loss % = ( Profit or Loss /Cost Price of the Article ) x 100
Example :
An article is bought at Rs. 400 and sold at Rs 500. What is the Profit/Loss percentage ?
Solution:
Here Since SP > CP, hence a profit occurs.
Profit = 500400 = 100
Profit % = ( Profit / CP ) * 100 % = ( 100/400 )*100% = 25%
One Important Formula :
Gain or Loss /Gainor Loss % = Cost Price / 100 = Selling Price / (100 + Gain%) or (100 – Loss%)
Example:
A 25% gain incurs a gain of 100rs. What is the Cost price of the article ?
Solution:
100/25 = CP/ 100
CP= 400
Concept : When two articles are sold at the same price for a gain of x% and another at a loss of x%, then the net transaction ends in a LOSS. The loss % of the whole scenario = (x/10)^{2 }
Example:
2 similar articles were sold at Rs 800. On one there was a 10% profit made, On the other a loss of 10% incurred. What is the net gain/loss in this transaction ?
Solution:
Total Loss = (10/10)^2 = 1%
Marked Price : This is done solely by the seller. He buys articles / products at a definite price (Cost Price) and then Marks up the price of the article / product . The price is raised above the original Cost Price hence it is called MARKED Price or MP.
Discount : It is that % cut that is provided to the customer on the marked price (MP). Remember, discount is always calculated on MP.
Selling price of an article = MP – Discount
Example :
The cost price of an article is Rs 400. It is marked up by 25%. And then a discount of 10% is given. What is the Profit/Loss percent engaged in the transaction ?
Solution :
Cost price = 400
Markup % = 25%
Marked Price = 400 + (25/100 )*400 = 400 + 100 = 500
Discount = 10%
Hence Selling Price = 90/100 * 500 = 450
SP > CP, hence a profit is incurred
Profit = 450400 = 50
Profit % = 50/ CP * 100 % = (50/400) *100 = 12.5%
Note : Discount is always calculated on MP. Selling price is the price after the discount is given on the article.
Profit & Loss Practice questions :
The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is:
Solution:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20  x).
(20  x ) * 100 / x = 25
= > 2000  100x = 25x
= > 125x=2000
= > x=16
By selling 45 lemons for Rs 40, a man loses 20 %. How many should he sell for Rs 24 to gain 20 % in the transaction ?
Solution:
Let S.P. of 45 lemons be Rs. x.
Then, 80 : 40 = 120 : x or x = 40 x 120 / 80= 60
For Rs.60, lemons sold = 45
For Rs.24, lemons sold =45/60 x 24= 18.
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Solution:
C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain = ( 80 x 100/ 1600) % = 5%
If books bought at prices ranging from Rs. 200 to Rs. 350 are sold at prices ranging from Rs. 300 to Rs. 425, what is the greatest possible profit that might be made in selling eight books ?
Solution:
Least Cost Price = Rs. (200 * 8 ) = Rs. 1600.
Greatest Selling Price = Rs. (425 * 8 ) = Rs. 3400.
Required profit = Rs. (3400  1600) = Rs. 1800.
A man purchased some chocolates at 80 per Rs 100 and same number of chocolates of other type at 120 per Rs. 100. He sold each chocolate per 1 rupee each, what is his profit/loss percentage?
Solution :
The first type of chocolate costs Rs. 100/80 rupees = 5/4 rupee.
The second type costs Rs. 100/120 = 5/6 rupee
Since he purchased both the chocolates in equal number, the Average cost per chocolate is = ( (5/4) + (5/6) ) /2 = 25/24
But he is selling each chocolate at Re. 1. So he get a loss of ((25/24) 1) / (25/24) =1/25
Percent loss = (1/25)*100 = 4% loss
Faulty Scale / Balance
Many a time dishonest sellers uses false scale and balances to sell the goods. They incorporate the balance with faulty weights /codes. The seller sells lesser amount of goods / items using these faulty balances. Hence gains a good percent of the total.
If the seller sells “x” gm of an item on 1 KG then the gain percent is calculated as :
Gain percent = (Difference / Actual) * 100%
= ((1000x)/x) *100%
Example :
A dishonest seller uses a faulty scale. His scale shows 1000 gms from 900 actual Weight. What is the profit percent of the seller ?
Solution:
Profit % = ((1000900)/900 )* 100% = (100/900) *100% = 11.11 %
Concept :
When false scale is used for buying as well as selling:
While purchasing if he gains x%, and at the time of selling it to the customer, he gains another y% , then the total profit % is given by :
P = [((100+x)*(100+y)/100) – 100 ] %
Successive Discounts
If there are successive discounts on an article , be them x% and y%, then the selling price of the article is = [ ((100x)/100)* ((100y)/100) ] * MP
If there are 3 successive discounts say of x% , y% , z% , then the selling price of the article will be :
= [ ((100x)/100)*((100y)/100)*((100z)/100)] * MP