Percentages Profit & Loss Partnerships Notes for Competitive Exam Preparation
Percentage:
"Percent" implies " for every hundred". This concept is developed to facilitate easier comparison of fractions by equalising denominator to hundred.
Example:-
7/11 as a percentage is represented as
((7/11)100)/100= 63.63% or 63 power of 7/11 %
Note:- Percentages an also be represented as decimal fractions. In such a case, it is effectively equivalent to proportion of the original quantity.
For Example, 20% is the same as 20/100 i.e, 0.2.
Any percentage can be expressed as a decimal fraction by dividing the percentage figure by 100.
Percentage Increase of Decrease of a quantity is the ratio expressed in percentage of the actual Increase or Decrease of the quantity and the original amount of the quantity.
For Example, if the production of rice went up from 225 Mt in 1993 to 242 Mt in 1994, then the percentage increase in rice production from 1993 to 1994 is calculated as follows..
Actual Increase = 242-225= 17 Mt
Percentage Increase= (Actual Increase from 1993 to 1994/ Actual Production of rice in 1993)X100
= (17/225)X 1000
=7.5 %
Ratio between any two quantities can also be expressed as percentage.
For Example, if the ratio of A and B is 3:2, we can say the ratio of A:B is 60%:40%
Whenever there is any percentage increase or decrease on a quantity is 1.15X350 = 402.5(where 1.15= 1+ 0.15, 0.15 being the decimal equivalent of 15%).
If the production in 1994 is given as 400 Mt and the increase from 1993 to 1994 is given to be 25%, then the production in 1993 will be equal to 400/1.25 (where 1.25= 1+0.25, 0.25 being the decimal equivalent of 25%).
Similarly, if there is a decrease of 12% on a quantity of 225, then the new quantity will be equal to 225 X 0.88(where 0.88= 1-0.12, 0.12 being the decimal equivalent of 12%).
If the production in 1994 is given as 400 Mt and it is a decrease of 13% from 1993, then the production in 1993 will be equal to 400/0.87 (where 0.87= 1-0.13, 0.13 being the decimal equivalent of 13%).
Worked Out Examples:
1) The price of one kilogram of rice was costing Rs. 15 in the year 1998. It has risen to Rs. 18 in the year 2000. What is the percentage increase in its price ?
Sol:-
Percentage increase= (Final Price - Initial Price)/Initial Price
=((18-15)/15)X100= (3/15)X100= 20%
2) The price of cooking oil rises by 25%. By what percentage should a consumer reduce his consumption in order to spend the same amount as earlier ?
Sol:-
Amount spent by the consumer = number of kilograms X price per kilogram
Let the number of kilograms and price per kilogram be X and Y respectively.
Original amount = Rs. XY
Increased price = 125/100 XY= Rs. 1.25 Y per kg.
Let the reduce quantity be X1kg.
X1 x 1.25Y= X*Y
X1=(100/125)X
if X is 100
X1=0.8*100= 80
Quantity reduced= 100-80=20%
Consumption is reduced to 20% when compared to the original consumption.
Profit and Loss:
In any business/commercial environment the most important concern is about the profit/loss of the transaction conducted.
The Selling Price (S.P) and the Cost Price(C.P) of an article determine the profit or loss made on the particular transaction.The computation is done as follow:
Profit= Sale Price- Cost Price = S.P-C.P.
Profit Percentage= ((S.P-C.P)/C.P)x100
= (Profit/C.P)x100
Loss= C.P-S.P.
Loss Percentage= (Loss/Cost Price)x 100.
It is customary to express profit/loss as percentage of Cost Price. However, in some problems it may be specifically be given that profit/loss percentage has been calculated on the selling price or the student may be asked to calculate the profit/loss percentage on the selling price. Unless such specific directions are given, the profit/loss percentage is always to be calculated on the cost price.
Marked Price of List Price is the price that is indicated or marked on the product or it is the price which is given in the price list. This is the price at which the product is intended to be sold. However, there can be some Discount given on this price and consequently, the actually Selling Price of the product may be less than the Marked Price.
Selling Price = Marked Price- Discount.
The amount of discount given can also be expressed as a percentage. Discount is always expressed as a percentage of the Marked Price or the List Price.
Discount Percent = (Marked Price - Selling Price)/Marked Price.
Worked Out Examples:
1) A trader buys one kilogram of tea at Rs.200 and sells at Rs.250. What is his profit percentage ?
Sol:-
Selling Price(S.P) = Rs. 250
Cost Price(C.P) = Rs. 200
Profit= S.P-C.P=250-200= Rs.50
Profit Percentage = (Profit/C.P)x100
= (50/200)x100
=25%
2) An article is sold at loss of 18%. If the article was sold at 12% profit, the trader would have earned Rs.60 more. What is the cost price of the article ?
Sol:-
Let C.P be Rs.X
S.P1=(100-18/100)X
= 0.82X
S.P2= (100+12/100)X
= 1.12X
Given that 1.12X-0.82X= 60
0.3X= 60
X= 200
Therefor Cost Price is Rs. 200/-
3) Raju sells an article to Harish at 20% profit and Harish sells it to Gopal at 30% loss. If Gopal pays Rs.210 for the article, what is the cost price of Raju ?
Sol:-
Let the cost price of Raju be Rs.X.
Cost Price of Harish= Selling Price of Raju = (120/100)X
Cost Price of Gopal = Selling Price of Harish = (70/100)(120/100)X
Therefore (70/100)(120/100)X
X= Rs.250.
Cost Price of Raju = Rs. 250.
Important Links:- Probability Notes for Competitive Exams
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