$$4\frac{1}{10}-\left[2\frac{1}{2}-\left\{\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right\}\right]$$​on simplification gives

Correct option is B

Given:

​$$4\frac{1}{10}-\left[2\frac{1}{2}-\left\{\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right\}\right]$$​​

Solution:

​$$4\frac{1}{10}-\left[2\frac{1}{2}-\left\{\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right\}\right] \\ \ \\ =\frac{41}{10}-\left[\frac{5}{2}-\left\{\frac{5}{6}-\left(\frac{2}{5}+\frac{3}{10}-\frac{4}{15}\right)\right\}\right] \\ \ \\ = \frac{41}{10}-\left[\frac{5}{2}-\left\{\frac{5}{6}-\left(\frac{12+9-8}{30}\right)\right\}\right] \\ \ \\ = \frac{41}{10}-\left[\frac{5}{2}-\left\{\frac{25-13}{30}\right\}\right] \\ \ \\ = \frac{41}{10}-\left[\frac{5}{2}-\left\{\frac{12}{30}\right\}\right] \\ \ \\ = \frac{41}{10}-\left[\frac{75-12}{30}\right] \\ \ \\ = \frac{123 - 63}{30} \\ \ \\ = \frac{60}{30} \\ \ \\ =2$$