Question : The difference of $5.\overline{76}$ and $2.\overline{3}$ is:
Option 1: $2.\overline{54}$
Option 2: $3.\overline{73}$
Option 3: $3.\overline{46}$
Option 4: $3.\overline{43}$
Correct Answer: $3.\overline{43}$
Solution :
$5.\overline{76} = 5 + \frac{76}{99}$
$2.\overline{3} = 2 + \frac{3}{9}$
Now,
$5 + \frac{76}{99} - 2 - \frac{3}{9}$
= $3 + (\frac{76}{99} - \frac{3}{9})$
= $3 + (\frac{43}{99})$
= $3\frac{43}{99}$
= $3.\overline{43}$
Hence, the correct answer is $3.\overline{43}$.
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