The value of $$\left(\frac{7}{8}\div5\frac{1}{4}\times7\frac{1}{5}-\frac{3}{20}of\frac{2}{3}\right)\div\frac{1}{2}+\left(\frac{3}{5}\times7\frac{1}{2}+\frac{2}{3}\div\frac{8}{15}\right)$$ is equal to 7 + k, where k =

Given : $$\left(\frac{7}{8}\div5\frac{1}{4}\times7\frac{1}{5}-\frac{3}{20}of\frac{2}{3}\right)\div\frac{1}{2}+\left(\frac{3}{5}\times7\frac{1}{2}+\frac{2}{3}\div\frac{8}{15}\right)=7+k$$

L.H.S. = $$\left(\frac{7}{8}\div5\frac{1}{4}\times7\frac{1}{5}-\frac{3}{20}of\frac{2}{3}\right)\div\frac{1}{2}+\left(\frac{3}{5}\times7\frac{1}{2}+\frac{2}{3}\div\frac{8}{15}\right)$$

= $$\left(\frac{7}{8}\div\frac{21}{4}\times\frac{36}{5}-\frac{1}{10}\right)\div\frac{1}{2}+\left(\frac{3}{5}\times\frac{15}{2}+\frac{2}{3}\div\frac{8}{15}\right)$$

= $$\left(\frac{7}{8}\times\frac{4}{21}\times\frac{36}{5}-\frac{1}{10}\right)\div\frac{1}{2}+\left(\frac{3}{5}\times\frac{15}{2}+\frac{2}{3}\times\frac{15}{8}\right)$$

= $$[(\frac{6}{5}-\frac{1}{10})\times2]+\frac{9}{2}+\frac{5}{4}$$

= $$\frac{11}{5}+\frac{9}{2}+\frac{5}{4}$$

= $$\frac{44+90+25}{20}=\frac{159}{20}=7+\frac{19}{20}$$

Comparing both sides, we get : $$k=\frac{19}{20}$$

=> Ans - (D)