A is 80% more than B and C is $$48\frac{4}{7}\% $$  less than the sum of A and B. By what percent is C less than A?

Solution (By Examveda Team)

$$\eqalign{ & {\bf{Given:}} \cr & {\text{A is }}80\% {\text{ more than B}} \cr & {\text{C is }}48\frac{4}{7}\% {\text{ less than A}} + {\text{B}} \cr & {\bf{Formula}}\,{\bf{used:}} \cr & 80\% \to \frac{4}{5} \cr & {\bf{Calculation:}} \cr & \Rightarrow {\text{A}} = \left( {1 + \frac{4}{5}} \right){\text{B}} = \frac{{9{\text{B}}}}{5} \cr & \Rightarrow {\text{C}} = \left( {100\% - 48\frac{4}{7}\% } \right)\left( {{\text{A}} + {\text{B}}} \right) \cr & \Rightarrow {\text{C}} = 51\frac{3}{7}\% \times \left( {\frac{{9B}}{5} + {\text{B}}} \right) \cr & \Rightarrow {\text{C}} = \frac{{3.6}}{7} \times \frac{{14{\text{B}}}}{5} \cr & \Rightarrow {\text{C}} = \frac{{7.2{\text{B}}}}{5} \cr & {\text{Difference between A and C}} = \frac{{1.8{\text{B}}}}{5} \cr & \Rightarrow {\text{Percentage}} = \frac{{\frac{{1.8{\text{B}}}}{5}}}{{\frac{{9{\text{B}}}}{5}}} \times 100 \cr & = 0.2 \times 100 \cr & = 20\% \cr & \therefore {\text{The required percentage}} = 20\% \cr & \cr & {\bf{Alternate}}\,{\bf{solution:}} \cr & {\text{Let the value of B be 100}} \cr & \Rightarrow {\text{A}} = 100 \times 180\% = 180 \cr & \Rightarrow \left( {{\text{A}} + {\text{B}}} \right) = 280 \cr & {\text{According to the question}} \cr & {\text{C}} = 51\frac{3}{7}\% {\text{ of }}280 \cr & \Rightarrow {\text{C}} = \frac{{360}}{{700}} \times 280 = 144 \cr & {\text{So, required }}\% = \frac{{180 - 144}}{{180}} \times 100\% = 20\% \cr & \therefore {\text{The required }}\% {\text{ is }}20\% \cr} $$