If a : b = c : d, prove that:
xa + yb : xc + yd = b : d

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Solution

Given, a/b = c/d
$\frac{x a}{y b}$ = $\frac{x c}{y d}$ (By compenendo)
$\frac{x a + y b}{y b}$ = $\frac{x c + y d}{y d}$
$\frac{x a + y d}{x c + y d}$ = $\frac{b}{d}$
– Hence Proved

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