The value of $5 \frac{1}{3} \div 1 \frac{2}{9} \times \frac{1}{4} (10 + \frac{3}{1 - \frac{1}{5}}) = ?$ ${\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) = ?$

115
2 $\frac{67}{25}$ $\frac{{67}}{{25}}$
3 $\frac{128}{11}$ $\frac{{128}}{{11}}$
4 $\frac{128}{99}$ $\frac{{128}}{{99}}$

Answer:- 1

Explanation:-

Solution:

\begin{aligned} According to question \\ 5 \frac{1}{3} \div 1 \frac{2}{9} \times \frac{1}{4} (10 + \frac{3}{1 - \frac{1}{5}}) \\ = \frac{16}{3} \div \frac{11}{9} \times \frac{1}{4} (10 + \frac{3}{\frac{4}{5}}) \\ = \frac{16}{3} \div \frac{11}{9} \times \frac{1}{4} (10 + \frac{15}{4}) \\ = \frac{16}{3} \times \frac{9}{11} \times \frac{1}{4} \times \frac{55}{4} \\ = \frac{48}{11} \times \frac{1}{4} \times \frac{55}{4} \\ = 15 \end{aligned}

$\eqalign{ & {\text{According to question}} \cr & {\text{5}}\frac{1}{3} \div 1\frac{2}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{1 - \frac{1}{5}}}} \right) \cr & = \frac{{16}}{3} \div \frac{{11}}{9} \times \frac{1}{4}\left( {10 + \frac{3}{{\frac{4}{5}}}} \right) \cr & = \frac{{16}}{3} \div \frac{{11}}{9} \times \frac{1}{4}\left( {10 + \frac{{15}}{4}} \right) \cr & = \frac{{16}}{3} \times \frac{9}{{11}} \times \frac{1}{4} \times \frac{{55}}{4} \cr & = \frac{{48}}{{11}} \times \frac{1}{4} \times \frac{{55}}{4} \cr & = 15 \cr}$