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# Note for Percentage - P by Placement Factory

• Percentage - P
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The term percent means “for every hundred”. It can best be defined as“A fraction whose denominator is 100 is called a percentage, and the numerator of the fraction is called the rate percent. E.g. A man saves 10% of his monthly income means ‘A man saves Rs 10 out of every Rs 100 of his income. Some of the important prime fractions represented in percentage terms are given below- Some important RulePercentage Page 1

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Rule-1 If Two values are respectively x% and y% more than a third value, then the second is of the3 third. Q Two numbers are respectively 25% and 50% more than the third. What percenta is the second is the third? Ans:- Required percentage value= Rule=2 If A is x% of C and B is y% of C, then A is % of B Q. Two numbers are respectively 20% and 60% less than a third number. What percent is the second of the first? Ans- Required number value= Rule=3 X% of a quantity is taken by the first, y% of the remaining is taken by the second and Z % of the remaining is taken by the third person. Now if the fund is left by an amount equal to a, then fund at the beginning was = Rule=4 at first, x% of the quantity is added, then y% of the increased quantity is added and again z% of the increased quantity is added. Now, the fund value becomes A, then initial amount was equal to= Q. A man had Rs 24000 in his bank account 2 years ago. In the first year, he deposited 20% of the amount in his bank account balance. In the second year, he Percentage Page 2

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deposited 25% of the increased amount in his account. What is the deposit amount of present in his bank account? Ans- Presently, the deposit amount in his bank account. Note- Above two rules are applicable for any identity in which there are changes for successive time periods, i.e. there may be continuous increase or decrease for successive time periods. For increase + sign is used and for decrease sign is used. Q The population of a town is 10000. It increase by 10% during the first year. During the second year it decreases by 20% and increases by 30% during the third year. What is the population of the town after 3 years? Ans- Population of the town after 3 years= Rules= 5 If the price of a commodity increase by R%, then the reduction in its consumption so as to keep the expenditure same is Rules -6 If the price of the commodity decrease by R%, then increase in consumption so as to keep the expenditure same is Q If the price of the sugar falls down by 20%, by how much percent must a household increase its consumption so as not to decrease expenditure on this item? Percentage Page 3

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Ans- Required percentage % = Note: =Above two rules are used to show increase and decrease relationship in percentage terms of two items. Q If A’s salary is 20% more than that of B, then how much percent is B’s salary then that of A ? Ans- Required percent Rule-7 If the value of a number is first increased by x% and then decreased by x%, the net change is a decrease and is equal to x% of x i.e. Rule 8 : If the value is first increased by x% and then decreased by y% then there is increase or decrease, according to the +ve or –ve Note- If orders of increase and decrease are changed, there will be no effect on the % changes. Q A shopkeeper marks the price of his goods 20% higher than its original price. Then, he allows a discount of 20%, what is his percentage profit or loss? Ans- here loss= Q The salary of an employee was first increased by 10% and there after decreased by 5%. What was the change in his salary in percentage terms? Percentage Page 4