Question

What number should be subtracted from each of the numbers 4, 10 and 28 so that the remainder may be in continued proportion? ​

Answer 1

Answer:

1 is the answer you need to subtract

Answer 2

Answer:

The number to be subtracted from each of the numbers 4, 10 and 28 so that they may be in continued proportion is 1.

Step-by-step explanation:

Three numbers are said to be in continued proportion if the ratio of first two numbers is equal to the ratio of last two numbers. That is, numbers a, b and c are in continued proportion if

$\dfrac{b}{a}=\dfrac{c}{b}$

Given the numbers 4, 10 and 28. Let $x$ be the number to be subtracted from each of these numbers, so that the remaining numbers, $4-x$, $10-x$ and $28-x$ are in continued proportion. Using the definition of continued proportion, we have

$\dfrac{10-x}{4-x}=\dfrac{28-x}{10-x}$

Now we can solve the above equation for $x$.

$(10-x)(10-x)=(28-x)(4-x)$

Expand both sides of the equation,

$100-20x+x^{2} =112-32x+x^{2}$

⇒ $\\100-20x=112-32x$

⇒ $-20x+32x=112-100$

⇒ $12x=12$

⇒ $x=\frac{12}{12}=1$