Question

The mean proportional of two numbers is 16 and the third proportional is 128. The larger number is ______.

Options

• 24

• 48

• 32

• 64

Answer 1

The mean proportional of two numbers is 16 and the third proportional is 128. The larger number is 32.

Explanation:

Let the two numbers be a and b,

The mean proportional of a and b is 16,

`sqrt(ab)` = 16

ab = 16²

ab = 256

a = `256/b`

The third proportional of a and b is 128

a, b, and 128 are in continued proportion

a : b = b : 128

`a/b = b/128`

b² = 128a

Substitute expression for a into the second equation:

b² = `128 xx (256/b)`

b³ = 128 × 256

b³ = 32768

b = `root3 (32768)`

= 32

Now find the value of a using a = `256/b`

a = `256/32`

= 8

∴ The larger number is 32.