The simple interest on a certain sum for $$4\frac{2}{9}$$​ years at the rate of 4.5% per annum is ₹8,778. What will be the amount payable on the same sum at the rate of 5.5% per annum simple interest in $$2\frac{5}{7}$$​ years?

Correct option is C

​$$\textbf{Given:}\\\text{Simple Interest on a certain sum for }4\frac{2}{9}\text{ years at }4.5\%\text{ p.a. }= ₹8,778\\\text{Rate for second case }=5.5\%\text{ p.a.}\\\text{Time for second case }=2\frac{5}{7}\text{ years}\\[1em]\textbf{Formula Used:}\\\\SI=\frac{P\times R\times T}{100}\\A=P+SI\\[1em]\textbf{Solution:}\\4\frac{2}{9}=\frac{38}{9}\\\qquad\\4.5\%=\frac{9}{2}\%\\[1em]8778=\frac{P\times \frac{9}{2}\times \frac{38}{9}}{100}\\[1em]8778=\frac{P\times 38}{200}\\[1em]8778=\frac{19P}{100}\\[1em]P=\frac{8778\times 100}{19}\\[1em]P=46,200\\[2em]5.5\%=\frac{11}{2}\%\qquad2\frac{5}{7}=\frac{19}{7}\\[1em]SI=\frac{46200\times \frac{11}{2}\times \frac{19}{7}}{100}\\[1em]SI=\frac{46200\times 11\times 19}{1400}\\[1em]SI=6,897\\[2em]A=P+SI\\[1em]A=46,200+6,897\\[1em]A=53,097\\[2em]\boxed{₹53,097}$$​​