Class 10 Maths Chapter 3 Notes

Important full class 10 maths chapter 3 notes in 10th Class Mathematics Urdu Medium by Mr. Tasneem Haider. These computerized notes are very helpful in the preparation of class 10 maths chapter 3 notes for students of the 10th class Mathematics and these are according to the paper patterns of all Punjab boards.

• Important class 10 maths chapter 3 notes pdf for all students of Punjab  Textbook Board.
• Define ratio, proportions and variations (direct and inverse).
• Find 3rd, 4th, mean and continued proportion.
• Important class 10 maths chapter 3 notes pdf download for all students of Punjab  Textbook Board.
• Apply theorems of invertendo, alternendo, componendo, dividendo and componendo & dividendo to find proportions.
• Define joint variation.
• Solve problems related to joint variation.
• Important class 10 maths notes chapter 3 for all students of Punjab  Textbook Board.
• Use k-method to prove conditional equalities involving proportions.
• Solve real life problems based on variations.
• Ratio, Proportions and Variations:
• Important class 10 notes maths chapter 3 for all students of Punjab  Textbook Board.
• (i) Define (a) ratio, (b) proportion and (c) variations (direct and inverse).
• (a) Ratio: A relation between two quantities of the same kind (measured in same unit) is called ratio. 
• Important class 10th chapter 3 maths notes for all students of Punjab  Textbook Board.
• If a and b are two quantities of the same kind and b is not zero, then the ratio of a and b is written as a : b or in fraction a / b e.g., if a hockey team wins 4 games and loses 5, then the ratio of the games won to games lost is 4:5 or in fraction 4 / 5
• Important class 10th maths chapter 3 notes for all students of Punjab  Textbook Board.
• Remember that: (i) The order of the elements in a ratio is important. (ii) In ratio a : b, the first term a is called antecedent and the second term b is called consequent. (iii) A ratio has no units.
• Example: Find the ratio of (i) 200gm to 700 gm  (ii) 1km to 600m
• Important math class 10 chapter 3 notes for all students of Punjab  Textbook Board.
• Solution: (1) Ratio of 200gm to 700 gm , 200 : 700 = 200 / 700 = 2 : 7 , Where 2 : 7 is the simplest (lowest) form of the ratio 200 : 700.
•  (ii) then or Ratio of 1km to 600m , Since 1km = 1000m , then 1000 : 600 = 1000 / 600 = 10 / 6 = 5 / 3 = 5: 3
• Important maths class 10 notes chapter 3 for all students of Punjab  Textbook Board.
• or  1km : 600m = 1000 : 600 = 1000 / 100 : 600 /100 = 10 : 6 = 5 : 3
• Example: Find a, if the ratios a + 3 : 7 + a and 4 : 5 are equal.
• Important maths notes class 10 chapter 3 for all students of Punjab  Textbook Board.
• Solution: Since the ratios a + 3 : 7 +a and 4 : 5 are equal. in fraction form a + 3 / 7 + a = 4 / 5 , 5 ( a + 3 ) = 4 (7+ a) , 5a + 15 = 28 + 4a , 5a - 4a = 28 - 15 , a = 13 , Thus the given ratios will be equal if a = 13.
• Important notes class 10 maths chapter 3 for all students of Punjab  Textbook Board.
• Example: If 2 is added in each number of the ratio 3 : 4, we get a new ratio 5 : 6. Find the numbers.
• Solution: Because the ratio of two numbers is 3 : 4 , Multiply each number of the ratio with x. Then the numbers be 3x, 4x and the ratio becomes 3x : 4x.
• Important notes for class 10 maths chapter 3 for all students of Punjab  Textbook Board.
•  Now according to the given condition  3x + 2 / 4x + 2 = 5 /6 , 6(3x+2) = 5(4x+2) , 18x + 12 = 20x + 10 , 18x - 20x = 10 - 12 , -2x = -2 , x = 1 , Thus the required numbers are: 3x = 3(1) = 3 , and 4x = 4(1) = 4. 
• Important notes of class 10 maths chapter 3 for all students of Punjab  Textbook Board.
• Proportion: A proportion is a statement, which is expressed as an equivalence of two ratios.  If two ratios a : b and c : d are equal, then we can write a : b = c : d , 
• Important notes of maths class 10 chapter 3 for all students of Punjab  Textbook Board.
• Where quantities a, d are called extremes, while b, c are called means. Symbolically the proportion of a, b, c and d is written as a : b : c : d  or  a : b = c : d
• Important 10th class math chapter 3 notes for all students of Punjab  Textbook Board.