The value of $$5\frac{1}{4} - \left[3\frac{1}{2} - \left\{\frac{5}{6} - \left(\frac{3}{5} \times \frac{1}{10} \div \frac{4}{15} \right)\right\}\right]$$​ is:

Correct option is A

Given:

We are to evaluate:

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

Solution:​

​$$\frac{21}{4} - \left[\frac{7}{2} - \left\{\frac{5}{6} - \left(\frac{3}{5} \times \frac{1}{10} \div \frac{4}{15} \right)\right\}\right]$$

=$$\frac{21}{4} - \left[\frac{7}{2} - \left\{\frac{5}{6} - \left(\frac{3}{5} \times \frac{1}{10} \times \frac{15}{4} \right)\right\}\right]$$

=$$\frac{21}{4} - \left[\frac{7}{2} - \left\{\frac{5}{6} - \frac {9}{40}\right\}\right]$$

$$=\frac{21}{4} - \left[\frac{7}{2} - \left\{\frac{100-27}{120}\right\}\right] \\ \ \\=\frac{21}{4} - \left[\frac{7}{2} - \frac {73}{120}\right] \\ \ \\=\frac{21}{4} - \left[\frac{420-73}{120}\right] \\ \ \\=\frac{21}4 - \frac{347}{120} \\ \ \\=\frac{630 - 347}{120} \\ \ \\=\frac { 283}{120}$$

= $$2 \frac{43}{120}$$​​