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Question
Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.
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Solution
Let x and y be two numbers
Mean proportional = 24
⇒ `sqrt(xy) = 24`
⇒ xy = 24 x 24 = 576
⇒ x = `(576)/y` ...(1)
Also 1536 is the third proportional then
x: y = y: 1,536
⇒ `x/y = y/(1,536)`
From(1), y2 = `1,536 xx (576)/y`
⇒ y3 = 1,536 x 576
⇒ y3 = 24 x 24 x 24 x 24
⇒ y = 24 x 24
⇒ y = 96
Again form(1), we get
x = `(576)/(96)`
= 6.
Hence, the required numbers are 6 and 96.
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