ABC26GN3021 · Ratio and Proportion
Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2006 · Marks: · Difficulty:
If $a:(b+c)=1: 3$ and $c:(a+b)=5: 7$, then $b:$ $(a+c)$ is equal to
(a)1 : 2
(b)2 : 3
(c)1 : 3
(d)2 : 1
Answer
Explanation
$$\begin{aligned} & \frac{a}{b+c}=\frac{1}{3} \Rightarrow a=\frac{b+c}{3} . \\ & \frac{c}{a+b}=\frac{5}{7} \Rightarrow 7 c=5 a+5 b=\frac{5(b+c)}{3}+5 b \\ & \Rightarrow 7 c-\frac{5}{3} c=5 b+\frac{5}{3} b \Rightarrow \frac{16 c}{3}=\frac{20 b}{3} \\ & \Rightarrow 16 c=20 b \Rightarrow b=\frac{4}{5} c . \\ & \quad a=\frac{b+c}{3}=\frac{\frac{4}{5} c+c}{3}=\frac{9 c}{5} \times \frac{1}{3}=\frac{3}{5} c . \\ & \therefore \frac{b}{a+c}=\frac{\left(\frac{4}{5} c\right)}{\left(\frac{3}{5} c+c\right)}=\frac{4 c}{5} \times \frac{5}{8 c}=\frac{1}{2}=1: 2 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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