Answer: Option C

Answer : Option C

Explanation :

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Solution 1
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$MF#%\begin{align}&\dfrac{3}{5} = 0.6\\\\
&\dfrac{6}{7} = 0.85 \quad \text{(Taken only the first two digits after the decimal point)} \end{align} $MF#%

Hence, the question is to find out a number which is greater than 0.6 and less than 0.85
The given choices are

$MF#%\begin{align}&\dfrac{1}{2} = 0.5\\\\
&\dfrac{2}{3} = 0.66 \quad \text{(Taken only the first two digits after the decimal point)} \\\\
&\dfrac{1}{3} = 0.33 \quad \text{(Taken only the first two digits after the decimal point)} \\\\
&\dfrac{7}{8} = 0.87 \quad \text{(Taken only the first two digits after the decimal point)}\end{align} $MF#%

$MF#%\text{Clearly, 0.66 = }\dfrac{2}{3}\text{ is the answer}$MF#%

--------------------------------------------------------------------------------------- Solution 2 --------------------------------------------------------------------------------------- LCM of 5, 7, 2, 3, 3, 8 = 840

$MF#%\begin{align}&\dfrac{3}{5} = \dfrac{504}{840}\\\\
&\dfrac{6}{7} = \dfrac{720}{840}\end{align} $MF#%

Hence, the question is to find out a number which is between the above numbers
The given choices are

$MF#%\begin{align}&\dfrac{1}{2} = \dfrac{420}{840}\\\\
&\dfrac{2}{3} = \dfrac{560}{840} \\\\
&\dfrac{1}{3} = \dfrac{280}{840} \\\\
&\dfrac{7}{8} = \dfrac{735}{840}\end{align} $MF#%

$MF#%\text{Clearly, }\dfrac{560}{840} = \dfrac{2}{3}\text{ is the answer}$MF#%