A) \[\frac{284}{497}\]
B) \[\frac{284}{495}\]
C) \[\frac{568}{990}\]
D) \[\frac{567}{990}\]
Correct Answer: C
Solution :
Given series 0.5737373?? = 0.5 + 0.073 + 0.00073 = 0.5 + \[\frac{73}{1000}+\frac{73}{100000}+....\] = \[0.5+73\left[ \frac{1}{1000}+\frac{1}{100000}+..... \right]\] = \[0.5+73\left[ \frac{1/1000}{1-\frac{1}{100}} \right]\]=\[0.5+\frac{73}{1000}.\frac{100}{99}=\frac{5}{10}+\frac{73}{990}\] = \[\frac{495+73}{990}=\frac{568}{990}\].
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