Question

Three positive numbers are in continued proportion. The middle number is 18. The 1st number is 4/9 times the third number. Find the third number.

Answer 1

Step-by-step explanation:

Let the 3 no.s be x, y, z

According to condition......

$\frac{x}{y} = \frac{y}{z}$

Where y (middle no. )= 18

and,

$x = \frac{4}{9} \times z$

$\frac{x}{18 } = \frac{18}{z} \\ x = \frac{324}{z} \\ \frac{4}{9} \times z \times z = 324 \\ {z}^{2} = \frac{324 \times 9}{4} \\ z = \sqrt{729} \\ z = 27$

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Answer 2

Required third number is 12.

Step-by-step explanation:

Let,

First number be a

Third number be 4a / 9, since third

number is 4/9 of the first number.

From the properties of ratio and proportion: If a, b and c are in continued proportion, then

=> a/b = b/c

=> axc=bxb

=> ac = b², where b is the middle term & a and c are the remaining terms.

Here,

Middle terms is 18, and the remaining terms are a and 4a / 9.

On the basis of the identity given above :

=> 18² = a × (4a/9)

=> 18² = a × a × 4/9

=> 18² = a² × (2/3)²

=> 18² (2a/3)²

=> 18 = 2a/3

=> 18 × 3/2=a

=> 27 = a

Hence,

=> Third number is: 4/9 × 27

=> Third number is : 4 × 3

=> Third number is : 12

Hence the required third number is 12.