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Question

A student was asked to simplify the following
$$\displaystyle \frac{7}{5-2\tfrac{2}{3}}\div \frac{3-\tfrac{2}{3-1\tfrac{1}{2}}}{4-1\tfrac{1}{2}}-\frac{5}{7}\times \left [ \frac{7}{10}+1\frac{1}{5}\times \frac{3\frac{1}{3}-2\frac{1}{2}}{2\frac{5}{21}-2} \right ]$$$$\displaystyle +\frac{\frac{3}{1.6}+\frac{5}{3.2}}{\frac{5}{4.8}+\frac{1}{9.6}}$$
His answer was $$\displaystyle 3\frac{1}{5}$$ Find the percentage error in the answer.


A
10%
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B
20%
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C
25%
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D
30%
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Solution

The correct option is C $$25\%$$
Given exp $$\displaystyle =\frac{7}{5-\tfrac{8}{3}}\div \frac{3-\tfrac{2}{3-\tfrac{3}{2}}}{4-\tfrac{3}{2}}$$
$$\displaystyle -\frac{5}{7}\left [ \frac{7}{10}+\frac{6}{5}\times \frac{\frac{10}{3}-\frac{5}{2}}{\frac{47}{21}-2} \right ]+\frac{\frac{30}{16}+\frac{50}{32}}{\frac{50}{48}+\frac{10}{96}}$$
$$\displaystyle =\frac{7}{\frac{7}{3}}\div \frac{3-\tfrac{2}{\frac{3}{2}}}{\frac{5}{2}}-\frac{5}{7}\left [ \frac{7}{10}+\frac{6}{5}\times \frac{\frac{20-15}{6}}{\frac{47-42}{21}} \right ]+\frac{\frac{15}{8}+\frac{25}{16}}{\frac{25}{24}+\frac{5}{48}}$$

$$\displaystyle 3\div \left [ \left ( 3-\frac{4}{3} \right )\times \frac{2}{5} \right ]-\frac{5}{7}\left [ \frac{7}{10}+\frac{6}{5}\times \frac{\frac{5}{6}}{\frac{5}{21}} \right ]+\frac{\frac{55}{16}}{\frac{55}{48}}$$

$$\displaystyle =3\div \left [ \frac{5}{3}\times \frac{2}{5} \right ]-\frac{5}{7}\left [ \frac{7}{10}+\frac{6}{5}\times \frac{21}{6} \right ]+\frac{48}{16}$$

$$\displaystyle =3\div \frac{2}{3}-\frac{5}{7}\left [ \frac{7}{10}+\frac{21}{5} \right ]+3$$

$$\displaystyle =\frac{9}{2}-\frac{5}{7}\times \frac{7}{10}-\frac{5}{7}\times \frac{21}{5}+3$$

$$\displaystyle =\frac{9}{2}-\frac{1}{2}-3+3=\frac{8}{2}=4$$

$$\displaystyle \therefore$$ Percentage error $$\displaystyle =\left ( \frac{4-3\tfrac{1}{5}}{3\frac{1}{5}}\times 100 \right )\%$$

$$\displaystyle =\left ( \frac{4-\tfrac{16}{5}}{\frac{16}{5}}\times 100 \right )\%=\left ( \frac{\frac{4}{5}}{\frac{16}{5}}\times 100 \right )\%=25\%$$

Mathematics

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