Question

When a number is subtracted from the number 8,12 and 20, the remainders are in continued proportion, Find the number ?

Answer 1

Given:

When a number is subtracted from the number 8, 12 and 20, the remainders are in continued proportion.

To find:

The number that is subtracted from the number 8, 12 and 20.

Solution:

Let "x" be the number subtracted from the number 8, 12 and 20.

So, we can write the ratio as follows:

$\dfrac{8-x}{12-x}=\dfrac{12-x}{20-x}$

(8 - x) (20 - x) = (12 - x) (12 - x)

160x - 8x - 20x + x² = 144 - 12x - 12x + x²

132x = 144 - 24x

132x + 24x = 144

156x = 144

x = 144/156

∴ x = 12/13

12/13 is a number that is subtracted from the number 8,12 and 20.

Answer 2

Given :

A number is subtracted from the number 8,12 and 20, the remainders are in continued proportion.

To Find:

Find the number ?

Solution:

Let number is subtracted is X, remaining number will be :

(8-X), (12 - X) , (20 - X)

Above number are in proportion, then:

$\mathbf{\dfrac{12-X}{8-X}=\dfrac{20-X}{12-X}}$

(12 - X)² = (20 - X) × (8-X)

On simplify:

144 -24 X + X² = 160 - 28 X + X²

On cancel out:

144 -24 X = 160 - 28 X

28 X - 24 X = 160 - 144

4 X = 16

So:

X = 4

So 4 is subtracted from the number 8,12 and 20, the remainders are in continued proportion.