Question

if a:b=c:d then ma + nc / mb + nb is equal to (1) m:n,(2)na:mb,(3) a:b,(4)md : nc​

Answer 1

Answer:

Given that,

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

Multiply the numerator & denominator on LHS by 'm' and on RHS by 'n', to get the following equation :

$\frac{ma}{mb} = \frac{nc}{nd}$

Doing cross-multiplication we get,

$\frac{ma}{nc} = \frac{mb}{nd}$

Adding 1 by both the sides we get,

$\frac{ma}{nc} + 1 = \frac{mb}{nd} + 1$

Which can be written as:

$\frac{ma + nc}{nc} = \frac{mb + nd}{nd}$

Again cross-multiplying we get,

$\frac{ma + nc}{mb + nd} = \frac{nc}{nd}$

Eliminating the common factor on RHS we get,

$\frac{ma + nc}{mb + nd} = \frac{c}{d}$

Given that,

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

Then,

$\frac{ma + nc}{mb + nd} = \frac{a}{b}$

The answer is a:b

Hope it helps! ! !