It is a question from ML aggarwal, class 10th, chapter 7, ratio and proportion, Avichal publication
In this question we have been given the two numbers and we have to find the mean proportional to them.
Question 4, 7.2
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Find the mean proportion of: (i) 5 and 80 (ii) 1/12 and 1/75 (iii) 8.1 and 2.5 (iv) (a – b) and (a3 – a2b), a ˃ b
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Solution:
(i) Consider x as the mean proportion of 5 and 80
5: x :: x: 80
It can be written as
x2 = 5 × 80 = 400
x = √400 = 20
Therefore, mean proportion of 5 and 80 is 20.
(ii) Consider x as the mean proportion of 1/12 and 1/75
1/12: x :: x: 1/75
It can be written as
x2 = 1/12 × 1/75 = 1/900
x = √1/900 = 1/30
Therefore, mean proportion of 1/12 and 1/75 is 1/30.
(iii) Consider x as the mean proportion of 8.1 and 2.5
8.1: x :: x: 2.5
It can be written as
x2 = 8.1 × 2.5 = 20.25
x = √20.25 = 4.5
Therefore, mean proportion of 8.1 and 2.5 is 4.5.
(iv) Consider x as the mean proportion of (a – b) and (a3 – a2b), a ˃ b
(a – b): x :: (a3 – a2b)
It can be written as
x2 = (a – b) (a3 – a2b)
So we get
x2 = (a – b) a2 (a – b)
x2 = a2 (a – b)2
Here
x = a (a – b)
Therefore, mean proportion of (a – b) and (a3 – a2b), a > b is a (a – b).