Imagine you and friend Sid got your report cards, and you scored 320 out of 400 whereas Sid scored 300 out of 360. You immediately say that, you have scored better than Sid, because 320 > 300. But, is that right? Report cards also have percentages written on them, and it shows that your percentage was 80% but Sid's percentage was 83.3%. So, this shows that, instead Sid has scored better.
Percentage is a method used to compare quantities. Percentages are numerators of fractions with the denominator 100. Percent is represented by the symbol  %.
Percent is derived from the Latin word ‘per centum’ meaning ‘per hundred' 
Example: What percent of ₹ 4500 is ₹ 9000?
Sol: Let us assume the percentage be Q,
Then, Q% of ₹ 4500 is ₹ 9000 => (Q/100) × 4500 = ₹ 9000
(4500Q/100) = ₹ 9000
45Q = ₹ 9000
Therefore, Q = ₹ 9000/45 = ₹ 200
Example: 30% of ₹ 360 = ________.
Sol: 30% of ₹ 360 = ₹ 108.
It can be written as = (30/100) × 360
= 10800/100
= ₹ 108
Example: 120 % of 50 km = ________.
Sol: 120 % of 50 km = 60 km.
It can be written as = (120/100) × 50
= 6000/100
= 60 km
Example: In a class of 50 students, 8 % were absent on one day. Find the number of students present on that day.
Sol: In a class of 50 students, 8 % were absent on one day. The number of students present on that day was 46.
From the question it is given that, number of students in the class = 50
Percentage of students who were absent on one day = 8%
Then, percentage of students who were present on one day = 100% – 8%
= 92%
So, 92% of 50
= (92/100) × 50
= 4600/100
= 46 students
Ratios help us to compare quantities and determine the relation between them. We write ratios in the form of fractions and then compare them by converting them into like fractions. If these like fractions are equal, then we say that the given ratios are equivalent.
Example: The ratio of Fatima’s income to her savings is 4: 1. The percentage of money saved by her is :
(a) 20% (b) 25% (c) 40% (d) 80%
Sol: (a) 20%
Let’s assume the ratio of Fatima’s income to her savings be 4x: 1x.
Then, the percentage of money saved by her is = (her savings/(income + savings)) × 100
= ( (1x / 4 x) + x ) × 100 = 1/5 x 100 = 20 %
Example: Reena’s mother said, to make idlis, you must take two parts rice and one part urad dal. What percentage of such a mixture would be rice and what percentage would be urad dal?
Sol: In terms of ratio we would write this as Rice: Urad dal = 2: 1.
Now, 2 + 1=3 is the total of all parts. This means 2/3 part is rice and 1/3 part is urad dal.
Then, percentage of rice would be (2/3) x 100 = (200/3) = 66.67%
Then, percentage of urad dal would be (1/3) x 100 = (100/3) = 33.33%
To compare fractional numbers, we need a common denominator. To convert a fraction into a percentage, multiply it by a hundred and then place the % symbol.
Percentages related to proper fractions are less than 100, whereas percentages related to improper fractions are more than 100.
Example: Out of 25 children in a class, 15 are girls. What is the percentage of girls?
Sol: Out of 25 children, there are 15 girls.
Therefore, the percentage of girls = 15/25 ×100 = 60.
There are 60% girls in the class.
Example: Convert 5/4 to percent.
Sol: We have, 5/4 x 100 = 125 %
To convert a decimal into a percentage:
Step 1: Convert the decimal into a fraction.
Step 2: Multiply the fraction by 100.
Step 3: Put a percent sign next to the number. Otherwise, shift the decimal point two places to the right.
Example: 2.5 = ________%
Sol:2.5 = 250 %
2.5 = 2.5 × 100
= 250%
Example: Convert the given decimals to per cents:
Sol: (a) 0.75
0.75 = 0.75 × 100 % = 75/100 × 100 % = 75%
(b) 49/50
49/50 = 49/50 x 100 = 98%
(c) 0.05
0.05 = 0.05 x 100 = 5%
A given percentage can be converted into fractions and decimals.
Examples:
Percent  2%  45% 
Fraction  2/100  45/100 
Decimal  0.02  0.45 
(a) To convert a percentage into a fraction:
Converting percentage into fraction
Step 1: Convert the mixed fraction percent into a proper fraction
Step 2: Now multiply the 1/100 to remove the percent symbol
Step 3: Reduce to the simplified fraction
Example: 225% is equal to
(a) 9: 4 (b) 4: 9 (c) 3: 2 (d) 2 : 3
Sol: (a) 9: 4
225% = (225/100)
(Because to remove the %, we have to divide the given number by 100.)
= 9/4
(b) To convert a percentage into a decimal:
Converting percentages into decimal
Step 1: Remove the percent sign.
Step 2: Divide the number by 100, or move the decimal point two places to the left in the numerator.
Example: Convert 77.5% into decimal
Sol: Dividing 77.5% by 100, we get;
77.5% = 77.5/100 = 7.75/10 = 0.775
Thus, 0.775 is the decimal equivalent of 77.5%.
Note: If we are given any two of the three quantities related to price, that is, CP, SP, and Profit or Loss percent, we can find the third.
Example: Mohini bought a cow for ₹ 9000 and sold it at a loss of ₹ 900. The selling price of the cow is ________.
Sol: Mohini bought a cow for ₹ 9000 and sold it at a loss of ₹ 900. The selling price of the cow is ₹ 8100
From the question it is given that,
The cost price of the cow (CP) = ₹ 9000
Loss = ₹ 900
We know that, Selling price (SP) = CP – loss
= 9000 – 900 = ₹ 8100
Example: Suhana sells a sofa set for Rs. making a profit of . What is the CP of the sofa?
Sol: Let the CP of the sofa be Rs. x
Example: If the price of sugar is decreased by 20%, then the new price of 3kg sugar, originally costing ₹ 120 will be _____.
Sol: If the price of sugar is decreased by 20%, then the new price of 3kg sugar originally costing ₹ 120 will be ₹ 96
From the question it is given that, price of 3kg sugar originally costing ₹ 120
The price of the sugar is decreased by 20%
Then, the new price of sugar = 120 – 20% of the original price
= 120 – (20/100) × 120 = 120 – (2400/100)
= 120 – 24 = ₹ 96
Example: Aahuti purchased a house for ₹ 50,59,700 and spent ₹ 40300 on its repairs. At what price should she sell the house to make a profit of 5%?
Sol: Aahuti purchased a house for ₹ 50,59,700 and spent ₹ 40300 on its repairs. To make a profit of 5%, she should sell the house for ₹ 5355000.
From the question it is given that,
CP of house purchased by Aahuti = ₹ 50,59,700
Amount spent to repair the house = ₹ 40,300
Total CP of house = ₹ 50,59,700 + 40,300 = ₹ 5100000
Profit % = (profit/CP) × 100 & profit = SP  CP
5 = ((SP – CP)/CP) × 100
5 = ((SP – 5100000)/5100000) × 100
(5 × 5100000)/100 = SP – 5100000 => SP = ₹ 5355000
Simple Interest is a method of calculating the amount of interest charged on a sum at a given rate and for a given period of time.
Example: Interest is typically expressed as a percentage for one year, denoted as per annum (p.a.). For instance, 10% p.a. implies that on every ₹100 borrowed, the borrower must pay ₹10 as interest for one year. This arrangement illustrates how the total amount owed is determined.
The general formula for simple interest over multiple years is derived by recognizing that the interest paid for one year on a principal amount (P) at an annual interest rate (R%) is given by
Therefore, the interest (I) paid for T years is expressed as . The total amount to be repaid at the end of T years is given by
If you are provided with any two of the quantities (I, P, T, R), you can use these formulas to calculate the remaining quantity.
Example: Find simple interest on ₹ 12500 at 18% per annum for a period of 2 years and 4 months.
Sol: Interest on ₹ 12500 at 18% per annum for a period of 2 years and 4 months is ₹ 5250.
From the question it is given that, Principal= ₹ 12500
Time = 2 years 4 months = (2 + (4/12)) = (2 + (1/3)) = 7/3 year
Rate = 18%
Then, we know the formula of Simple interest SI = (P × R × T)/100
SI= (12500 × 18 × (7/3)) /100
SI = ₹ 5250
Example: The difference of interest for 2 years and 3 years on a sum of ₹ 2100 at 8% per annum is _________.
Sol: The difference of interest for 2 years and 3 years on a sum of ₹ 2100 at 8% per annum is ₹ 168.
From the question it is given that, P = ₹ 2100 ,Time = 2 years, Rate = 8%
Then, we know the formula of Simple interest SI = (P × R × T)/100
SI = (2100 × 2 × 8)/100 = 33600/100 = ₹ 336
Then, taking Time = 3 years, simple interest is
SI= (2100 × 3× 8)/100 = 50400/100 = ₹504
The difference of interest for 2 years and 3 years = 3 years – 2 years
= ₹ 504 – ₹ 336
= ₹ 168
76 videos345 docs39 tests

1. How do you convert ratios into percentages? 
2. How can you convert fractional numbers into percentages? 
3. What is the formula to convert decimals into percentages? 
4. How do you convert percentages into fractions or decimals? 
5. How can you calculate profit or loss as a percentage? 

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