Question

When a number is subtracted from the number 8 12 20 the remainder are in continued proportion?

Answer 1

Answer:the number that shoud be subtracted is 4.

Step-by-step explanation:

Answer 2

Concept:

A continued proportion is a collection of three or more quantities, each of which has the same ratio to the one before it.

Given:

The given numbers are 8, 12, 20.

Find:

The number that should be subtracted from the numbers such that the remainder are in continued proportion.

Solution:

If all three numbers p, q, and r are in proportion, the three numbers are said to be in continuing proportion.

This can be mathematically represented as- $a : b : : b : c.$

Let the least number that can be subtracted be x.

$(8-x):(12-x)::(12-x):(20-x)$

$\frac{(8-x)}{(12-x)} =\frac{(12-x)}{(20-x)}$

$(8-x)(20-x)=(12-x)^{2}$

$160-8x-20x+x^{2} =144+x^{2} -24x\\28-24x=160-144\\4x=16\\x=4$

After subtracting 4 the numbers are 4, 8, 16.

∵ $4:8::8:16$, they are in continued proportion.

∴ 4 can be subtracted from the numbers 8 12 20 so that the remainder are in continued proportion.