A) \[24:42:49\]
B) \[4:6:7\]
C) \[4:6:11\]
D) \[24:42:73\]
Correct Answer: D
Solution :
\[A:B=(4:7)\times 6\to 24:42\] \[B:C=(6:7)\times 7\to 42:49\] \[A:B:C=24:42:49\] \[\frac{A}{B}=\frac{24}{42}\,\,\,\Rightarrow A=\frac{24}{42}B\] ?. (i) \[\frac{B}{C}=\frac{42}{49}\,\,\,\Rightarrow B=\frac{42}{49}C\] ?. (ii) \[A:B:(C+A)=\frac{24}{42}B:B:\left( \frac{49}{42}+\frac{24}{42} \right)B\] \[=\,\,\,\,\underline{\,\mathbf{24:42:73}}\]
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