Given that a:b::c:d, then which of the following follows Componendo and Dividendo property?

$d (a - b) = b (c - d)$

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$(a - b) : b = (c - d) : d$

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$\frac{a - b}{a + b} = \frac{c - d}{c + d}$

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Both a and b

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Solution

The correct option is C
$\frac{a - b}{a + b} = \frac{c - d}{c + d}$

When a, b, c, and d are in proportion i.e. when a : b :: c : d,
then $\frac{a}{b} = \frac{c}{d}$

Applying componendo and dividendo,

$\frac{a - b}{a + b} = \frac{c - d}{c + d}$

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Similar questions

If (a + b +c + d) (a -b- c+ d)

=(a + b- c- d) (a -b+c- d);

prove that : a : b =c : d.

For four numbers a, b, c, d if a : b = c : d, then b : a = d : c. Which property of proportion is this?

a : b :: c : d

(a - b) : b :: (c - d) : d .

a, b, c

d

∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & b & c & d b & a & d & c c & d & a & b d & c & b & a \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = (a + b + c + d) (a - b + c - d) (a - b - c + d) (a + b - c - d)

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