Simplification - Aptitude MCQ Questions and Solutions with Explanations

$$\eqalign{ & {\text{According to the question}} \cr & \frac{5}{{1\frac{7}{8}{\text{of 1}}\frac{1}{3}}} \times \frac{{2\frac{1}{{10}}}}{{3\frac{1}{2}}}{\text{ of 1}}\frac{1}{4} \cr & \Rightarrow \frac{5}{{\frac{{15}}{8} \times {\text{ }}\frac{4}{3}}} \times {\text{ }}\frac{{21}}{{10}} \times \frac{2}{7} \times \frac{5}{4} \cr & \Rightarrow 2 \times \frac{3}{4} \cr & \Rightarrow \frac{3}{2} \cr & \Rightarrow 1\frac{1}{2} \cr} $$

$$\eqalign{ & \frac{{225}}{{836}} \times \frac{{152}}{{245}} \div 1\frac{{43}}{{77}} \cr & = \frac{{225}}{{836}} \times \frac{{152}}{{245}} \div \frac{{120}}{{77}} \cr & = \frac{{225}}{{836}} \times \frac{{152}}{{245}} \times \frac{{77}}{{120}} \cr & = \frac{3}{{28}} \cr} $$

$$\eqalign{ & \frac{3}{2} \times \frac{{11}}{5} \div \left( {\frac{{25}}{{44}} \times \frac{{11}}{5}} \right) \div \frac{{33}}{{15}} \cr & = \frac{3}{2} \times \frac{{11}}{5} \div \frac{5}{4} \div \frac{{33}}{{15}} \cr & = \frac{3}{2} \times \frac{{11}}{5} \times \frac{4}{5} \times \frac{{15}}{{33}} \cr & = \frac{6}{5} \cr & = 1\frac{1}{5} \cr} $$

$$\eqalign{ & {\text{Given expression,}} \cr & \frac{{81}}{8}\,of\,\frac{{12}}{{15}} \div \frac{{35}}{{36}}\,of\,\frac{{20}}{{49}} \cr & = \frac{{81}}{{10}} \div \frac{{25}}{{63}} \cr & = \frac{{81}}{{10}} \times \frac{{63}}{{25}} \cr & = \frac{{5103}}{{250}} \cr & = 20\frac{{103}}{{250}}\, \cr} $$

$$\eqalign{ & {\text{According to the question,}} \cr & \sqrt {\frac{{{{\left( {0.03} \right)}^2} + {{\left( {0.21} \right)}^2} + {{\left( {0.065} \right)}^2}}}{{{{\left( {0.003} \right)}^2} + {{\left( {0.021} \right)}^2} + {{\left( {0.0065} \right)}^2}}}} \cr & = \sqrt {\frac{{0.0009 + 0.0441 + 0.004225}}{{0.000009 + 0.000441 + 0.00004225}}} \cr & = \sqrt {\frac{{0.049225}}{{0.00049225}}} \cr & = \sqrt {100} \cr & = 10 \cr} $$

$$\eqalign{ & {\text{According to the question,}} \cr & \sqrt {0.01} + \sqrt {0.81} + \sqrt {1.21} + \sqrt {0.0009} \cr & = 0.1 + 0.9 + 1.1 + 0.03 \cr & = 2.13 \cr} $$

$$\eqalign{ & {\text{According to the question,}} \cr & \sqrt {\frac{{0.342 \times 0.684}}{{0.000342 \times 0.000171}}} \cr & = \sqrt {\frac{{342 \times 684 \times 1000000}}{{342 \times 171}}} \cr & = \sqrt {4 \times 1000000} \cr & = 2 \times 1000 \cr & = 2000 \cr} $$

$$\eqalign{ & {\text{According to the question,}} \cr & \sqrt {0.00060516} {\text{ }} \cr & \Rightarrow \sqrt {\frac{{60516}}{{100000000}}} \cr & \Rightarrow \frac{{246}}{{10000}} \cr & \Rightarrow 0.0246 \cr} $$

$$\eqalign{ & {\text{Given expression,}} \cr & \frac{{\left( { - \frac{2}{3} - \frac{1}{2}} \right) + \left( {\frac{4}{5} + \frac{1}{5}} \right) + \left( {\frac{3}{4} - \frac{1}{2}} \right)}}{{\left( {\frac{2}{3} - \frac{4}{3} + \frac{1}{3}} \right) - \left( {\frac{1}{5} + \frac{4}{5}} \right) + \frac{1}{2}}} \cr & = \frac{{ - 1 + 1 + \frac{1}{4}}}{{ - \frac{1}{3} - 1 + \frac{1}{2}}} \cr & = \frac{{\frac{1}{4}}}{{\frac{{ - 2 - 6 + 3}}{6}}} \cr & = \frac{{\frac{1}{4}}}{{ - \frac{5}{6}}} \cr & = \frac{1}{4} \times \left( { - \frac{6}{5}} \right) \cr & = - \frac{3}{{10}} \cr} $$

$$\eqalign{ & {\text{Let,}} \cr & \frac{5}{3} \div \frac{2}{7} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \div \frac{1}{6} \cr & {\text{Then,}} \cr & \frac{5}{3} \times \frac{7}{2} \times \frac{x}{7} = \frac{5}{4} \times \frac{2}{3} \times 6 \cr & \Leftrightarrow \frac{5}{6}x = 5 \cr & \Leftrightarrow x = \left( {\frac{{5 \times 6}}{5}} \right) \cr & \Leftrightarrow x = 6 \cr} $$