Question : The value of $\frac{3}{70}+\frac{1}{42}+\frac{1}{66}+\frac{3}{286}+\frac{1}{130}+\frac{1}{170}$ is:
Option 1: $\frac{7}{85}$
Option 2: $\frac{11}{85}$
Option 3: $\frac{9}{85}$
Option 4: $\frac{3}{85}$
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Correct Answer: $\frac{9}{85}$
Solution :
$\frac{3}{70}+\frac{1}{42}+\frac{1}{66}+\frac{3}{286}+\frac{1}{130}+\frac{1}{170}$
$=\frac{18+10}{420}+\frac{13+9}{858}+\frac{1}{130}+\frac{1}{170}$
$=\frac{28}{420}+\frac{22}{858}+\frac{1}{130}+\frac{1}{170}$
$=\frac{1}{15}+\frac{1}{39}+\frac{1}{130}+\frac{1}{170}$
$=\frac{1}{15}+\frac{10+3}{390} +\frac{1}{170}$
$=\frac{1}{15}+\frac{13}{390} +\frac{1}{170}$
$=\frac{1}{15}+\frac{1}{30} +\frac{1}{170}$
$=\frac{34+17+3}{510}$
$=\frac{54}{510}$
$=\frac{9}{85}$
Hence, the correct answer is $\frac{9}{85}$.
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