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ReadDiscussView DiscussionImprove ArticleSave ArticleLike ArticleIn mathematics, a percentage is a number or ratio expressed as a fraction of 100. The word percentage is derived from the Latin word per centum which means by the hundred. The percentage is depicted using the symbol %. It has no unit of measurement and is a dimensionless number. The percentage can be represented either in fractional form or decimal form.Percentage FormulaIt is calculated by dividing the value by the total value and multiplying the result obtained by 100. Percentage (%) = (Valuetotal value) × 100 %Note: If P is r% more than Q, then Q is (r(100+r) × 100 less than PPercentage ChangePercentage change is calculated when there is a change in the value of a quantity over a period of time. Percentage change is calculated in terms of percentage increase and percentage decrease. For calculating the percentage change, we have to divide the change in value by the original value and then multiply the obtained value by 100.Percentage change = (change in value)original value × 100Where, Change in value = New value – original valuePercentage increase Percentage increase means the percentage change in the value of a quantity when it is increased over a period of time. It is calculated by subtracting the original value from the new value, dividing it by the original value, and then multiplying the resultant with 100. The formula for the percentage increase is given as,Percentage Increase = (New value – Original value)Original value × 100Note: If a value is increased by x% then the new value is (100 + x)% of the original amount.Percentage decreasePercentage decrease means the percentage change in the value of a quantity when it is decreased over a period of time. It is calculated by subtracting the new value from the original value, dividing it by the original value, and then multiplying the resultant by 100. The formula for the percentage decrease is given as,Percentage decrease = (Original value – New value)Original value × 100 Note: If a value is decreased by x%, then the new value is (100 – x)% of the original amount.Sample ProblemsProblem 1: A boy obtained 820 marks out in the examination out of 900 marks. Calculate the percentage of the marks obtained by the boy.Solution: Given, Number of marks obtained = 820Maximum marks = 900Percentage of marks = (820900) × 100⇒ Percentage = (0.9112) × 100Hence, the percentage of marks obtained by the boy is 91.12%Problem 2: Geethas weight is 25% more than that of Fathima. If Fathimas weight is 56 kg, then how much percent of Fathimas weight is less than that of Geetha?Solution:Given data, Fathimas weight = 60 kgGeethas weight is 25% more than that of Fathima.Hence, Geethas weight = 56 + 56 × (¼) = (56 + 16) kg = 72 kg.Required percentage = (72 – 56)72 × 100 =22.22%Hence, the weight of Fathima is 22.22% less than that of Geetha.Problem 3: Calculate the percentage increase if the price of the cooking oil of ₨ 150 increased to ₨ 180.Solution:Given data, Original price of the oil = ₨ 150New price of the oil = ₨ 180Change in the value of price = ₨ 180 – ₨ 150 = ₨ 30Percentage increase = (change in value)original value × 100⇒ Percentage increase = (30150) × 100 = 20 %Hence, the percentage increase in the price of the cooking oil is 20%Problem 4: The price of a mobile phone increases every year by 20%. If the present price is ₨ 15000, then what was the price (in ₨.) 3 years ago?Solution:Let the price of the mobile phone 3 years ago be PPrice of the mobile phone, 2 years ago = P + 20% of P = P + (20100)P = 1.20PPrice of the mobile phone, one year ago = 1.20 P + 20% of (1.2 P) = 1.20 P + 0.24P = 1.44 PPresent price of the mobile = 1.44 P + 20% of (1.44 P) = 1.44 P + 0.288 P = 1.728 P⇒ 1. 728 P = 15000⇒ P = ₨ 8680.55Hence, the price of the mobile phone 3 years ago was ₨ 8680.55Problem 5: Calculate the percentage change if the price of a dozen eggs decreased from ₨ 60 to ₨ 50.Solution:Given data, Original price of a dozen eggs = ₨ 60New price = ₨ 50Change in the value of the price = ₨ 60 – ₨ 50 = ₨ 10Percentage change = (decrease in price)original value × 100⇒ Percentage change = (1060) × 100 = 16.67%Hence, the percentage change in the price of a dozen eggs is 16.67%Problem 6: Ravis savings amount was ₨ 5000 in the month of January. His savings decreased to ₨ 3800 in the month of February. Calculate the percentage decrease in his savings.Solution:Given data, Ravis savings amount in January = 5000Ravis savings amount in February = 3800Decrease in his savings = 5000 – 3800 = 1200⇒ Percentage decrease = (decreased savings)original value × 100Now, percentage decrease in his savings = () 100 = 24%Problem 7: A number is increased by 25% and then decreased by 25%. Find the net increase or decrease percent.Solution:Let the number be 100.The number is increased by 25%We know that, if a value is increased by x% then the new value is (100 + x)% of the original amount.⇒ Now, the increased number = (100 + 25)% of 100 = (125100) × 100 = 125The number is now decreased by 25%We know that, if a value is decreased by x%, then the new value is (100 – x)% of the original amount.⇒ Now, the decreased number = (100 – 25)% of 125 = (75100) ×125 = 93.75⇒ Net decrease = 100 – 93.75 = 6.25Hence, the number is decreased by 6.25%
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