Question

If x:y=a:b, then by which property of equal ratio is x:a=y:b a)invertendo b) alternendo c)componendo d)dividendo ​

Answer 1

If $\mathsf{x:y=a:b}$, they by alternendo property of equal ratio, we can obtain $\mathsf{x:a=y:b}$.

Step-by-step explanation:

The given ratio is $\mathsf{x:y=a:b}$

$\mathsf{\Rightarrow \dfrac{x}{y}=\dfrac{a}{b}}$ [since ratio means division]

$\mathsf{\Rightarrow \dfrac{x}{a}=\dfrac{y}{b}}$ [altering sides for $\mathsf{y}$ and $\mathsf{a}$ ]

$\mathsf{\Rightarrow x:a=y:b}$

So, $\boxed{\mathsf{x:y=a:b\Rightarrow x:a=y:b}}$

Other properties of equal ratio:

Invertendo.

$\quad\mathsf{a:b=c:d\Rightarrow b:a=d:c}$

Componendo.

$\quad\mathsf{a:b=c:d\Rightarrow (a+b):b=(c+d):d}$

Dividendo.

$\quad\mathsf{a:b=c:d\Rightarrow (a-b):b=(c-d):d}$

Componendo et Dividendo.

$\quad\mathsf{a:b=c:d\Rightarrow (a+b):(a-b)=(c+d):(c-d)}$