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.

Answer 1

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.