Question

Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.

Answer 1

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.