If \( \Large \frac{a}{b}=\frac{2}{3}\ and\ \frac{b}{c}=\frac{4}{5} \) , then the ratio \( \Large \frac{a+b}{b+c} \) equal to:
Correct Answer: A) \( \Large \frac{20}{27} \) |
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Description for Correct answer:
\( \Large \frac{a}{b}=\frac{2}{3}\ and\ \frac{b}{c}=\frac{4}{5}\ (given)\ or\ \frac{c}{b}=\frac{5}{4} \)
Therefore, \( \Large \frac{a+b}{b+c}=\frac{b \left(\frac{a}{b}+1\right) }{b \left(\frac{c}{b}+1\right) } = \frac{\frac{a}{b}+1}{\frac{c}{b}+1} \)
= \( \Large \frac{ \left(\frac{2}{3}+1\right) }{ \left(\frac{5}{4}+1\right) } = \frac{\frac{5}{3}}{\frac{5+4}{4}} \)
= \( \Large \frac{5 \times 4}{3 \times 9} = \frac{20}{27} \)
Therefore, \( \Large \frac{a+b}{b+c} = \frac{20}{27} \)
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