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  1. Find the third proportional of the following: (i) 0.5, 0.25. (ii) a 2 2 b, ab 2 2. (iii) x y x y + y x y x, x y x y. 5. (i) If the mean proportional of a and c is b then prove that a, c, a 2 2 + b 2 2 and b 2 2 + c 2 2 are proportional.

  2. Q.1 Two numbers are in the ratio 3 : 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers. Q2 The work done by (x - 3) men in (2x + 1) days and the work done by (2x + 1) men in (x + 4) days are in the ratio 3 : 10. Find the value of x.

  3. We will learn how to find the mean and third proportional of the set of three numbers. If x, y and z are in continued proportion then y is called the mean proportional (or geometric mean) of x and z. If y is the mean proportional of x and z, y^2 = xz, i.e., y = +\(\sqrt{xz}\).

  4. Third Proportional Example 1. Find the third proportion to 6 and 12? Explanation: To find third proportional of any two numbers let say a and b be two numbers and c is in third proportion with a and b. Then, a : b = b : c. Let, the third proportion to 6 and 12 be a. 6 : 12 :: 12 : a (Product of Extremes= Product of Means) Here, Extremes are= 6 ...

  5. Third Proportional. Similar to the f=definition of the fourth proportional, we define the term known as the third proportional. The third proportional of a proportion is the second term of the mean terms. For example, if we have a:b = c:d, then the term ‘c’ is the third proportional to ‘a’ and ‘b’. Mean Proportional

  6. (1) Find the mean proportion between 4 and 9. (2) Find the third proportional to 12 and 30. Solution: (1) Let the mean proportion be X => 4, X and 9 are in continued proportion. 4: X = X: 9 X × X = 4 x 9 X2 = 36 X = 6 Ans. (2) Let X be the third proportional => 12, 30 and X are in continued proportion

  7. Proportional Relationship Worksheets help students to understand proportion and ratios and proportional relationships, ratios, and proportions. Children can download the pdf format of these easily accessible Proportional Relationship worksheets to practice and solve questions for free.

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