question_answer 45)

Jaidev takes \[\frac{35}{9}\] minutes to walk across the school ground. Rahul takes \[\begin{align} & 9\overline{)35(}3 \\ & \,\,\,\,\frac{27}{\underline{\,8\,\,\,\,\,\,}} \\ \end{align}\]minutes to do the same. Who takes less time and by what fraction?

Answer:

Time taken by Jaidev to walk across the school ground \[\therefore \] and time taken by Rahul to walk across the school ground \[\frac{35}{9}=3\frac{8}{9}\] Now, equivalent fractions or\[\frac{8}{9}\] are \[7\frac{3}{4}\] i.e. \[5\frac{6}{7}\] and equivalent fractions of\[2\frac{5}{6}\] are \[10\frac{3}{5}\] i.e. \[9\frac{3}{7}\] Here, equivalent fractions\[8\frac{4}{9}\]and \[\frac{\text{(Whole }\!\!\times\!\!\text{ Denominator)+Numerator}}{\text{Denominator}}\]have same denominators. \[7\frac{3}{4}=7+\frac{3}{4}=\frac{7\times 4+3}{4}=\frac{31}{4}\] \[6\frac{6}{7}=5+\frac{6}{7}=\frac{5\times 7+6}{7}=\frac{41}{7}\] \[2\frac{5}{6}=2+\frac{5}{6}=\frac{2\times 6+5}{6}=\frac{17}{6}\] \[10\frac{3}{5}=10+\frac{3}{5}=\frac{10\times 5+3}{5}=\frac{53}{5}\] Now, \[9\frac{3}{5}=9+\frac{3}{7}=\frac{9\times 7+3}{7}=\frac{66}{7}\] Hence, Rahul takes less time by \[8\frac{4}{9}=8+\frac{4}{9}=\frac{8\times 9+4}{9}=\frac{76}{9}\]