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Question
6 is the mean proportion between two numbers x and y and 48 is the third proportional of x and y. Find the numbers.
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Solution
6 is the mean proportion between two numbers x and y,
`i.e 6 = sqrt(xy)`
So, 36 = xy ...(1)
It is given that 48 is the third proportional to x and y
So, y2 = 48x … (2)
From (1) and (2), we get
`y^2 = 48 (36/y) => y^3 = 1728`
Hence, y = 12
`:. x = 36/y = 36/12 = 3`
Thus, the required numbers are 3 and 12.
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