Question : The value of $\frac{\frac{1}{3}+[4 \frac{3}{4}–(3 \frac{1}{6}–2 \frac{1}{3})]}{(\frac{1}{5} \text { of } \frac{1}{5} \div \frac{1}{5}) \div(\frac{1}{5} \div \frac{1}{5} \times \frac{1}{5})}$ lies between:
Option 1: 10.2 and 10.8
Option 2: 4.2 and 4.4
Option 3: 8.2 and 8.8
Option 4: 0.4 and 0.9
Correct Answer: 4.2 and 4.4
Solution :
Given: $\frac{\frac{1}{3}+[4 \frac{3}{4}–(3 \frac{1}{6}–2 \frac{1}{3})]}{(\frac{1}{5} \text { of } \frac{1}{5} \div \frac{1}{5}) \div(\frac{1}{5} \div \frac{1}{5} \times \frac{1}{5})}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–(\frac{19}{6}– \frac{7}{3})]}{(\frac{1}{25} \div \frac{1}{5}) \div(\frac{1}{5} \times 5 \times \frac{1}{5})}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–(\frac{19–7\times 2}{6})]}{(\frac{1}{25} \times 5) \div(\ \frac{1}{5})}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–\frac{19–14}{6}]}{\frac{1}{5} \div\ \frac{1}{5}}$
$=\frac{\frac{1}{3}+[ \frac{19}{4}–\frac{5}{6}]}{\frac{1}{5} \times 5}$
$=\frac{\frac{1}{3}+[ \frac{57–10}{12}]}{1}$
$=\frac{1}{3}+\frac{47}{12}$
$=\frac{4+47}{12}$
$=\frac{51}{12}$
$=4.25$
Hence, the correct answer is 4.2 and 4.4.
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