MAT Exam 2023 Paper

Concept:Simplify the given nested fractions carefully by solving the inner brackets first.Explanation:Convert the mixed fraction: $1\frac{1}{7} = \frac{8}{7}$.Simplify the fractional term in the numerator:$\frac{\frac{2}{5}}{1-\frac{1}{25}} = \frac{\frac{2}{5}}{\frac{24}{25}} = \frac{2}{5} \times \frac{25}{24} = \frac{5}{12}$.So the numerator becomes:$\frac{8}{7} - \frac{2}{3} + \frac{5}{12} = \frac{96 - 56 + 35}{84} = \frac{75}{84}$.Now simplify the inner bracket in the denominator:$\frac{\frac{2}{5}}{1-\frac{2}{5}} = \frac{\frac{2}{5}}{\frac{3}{5}} = \frac{2}{3}$.Therefore, the bracket becomes:$\frac{1}{3} - \frac{2}{3} = -\frac{1}{3}$.So the denominator is:$1 - \frac{1}{7}\left(-\frac{1}{3}\right) = 1 + \frac{1}{21} = \frac{22}{21}$.Hence, the whole expression is:$\frac{\frac{75}{84}}{\frac{22}{21}} = \frac{75}{84} \times \frac{21}{22} = \frac{75}{88}$.Answer:$\frac{75}{88}$Thus, the correct option is D.