Question

If a:(b+c)=1:4 and c:(a+b)=5:7then b:(a+c)is
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Answer 1

Answer:

$\frac{b + c}{a} = \frac{4}{1}$

adding 1 both side,

$\frac{a + b + c}{a} = 5 \: \: \: i.e \: \: \: \frac{a}{a + b + c} = \frac{1}{5} .....(i)$

now,

$\frac{a + b}{c} = \frac{7}{5}$

adding 1 both side,

$\frac{a + b + c}{c} = \frac{12}{5} \: \: \: \: \: i.e \: \: \: \: \frac{c}{a + b + c} = \frac{5}{12}..(ii)$

adding (i) & (ii),. we get

$\frac{a + c}{a + b + c} = \frac{1}{5} + \frac{5}{12} = \frac{12 + 25}{60} = \frac{37}{60}$

so,

$\frac{a + b + c}{a + c} = \frac{60}{37}$

substracting 1 both side, we get

$\frac{b}{a + c} = \frac{60 - 37}{37} = \frac{23}{37}$

Ans.

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