A monthly return railway ticket cost 25 percent more than a single ticket. A week's extension can be had for the former by paying 5 percent of the monthly ticket's cost. If the money paid for the monthly ticket (with extension) is Rs. 84, the price of the single ticket is :

Solution(By Examveda Team)

Let the cost of a single ticket be Rs. $$x$$
The, cost of monthly return ticket :
$$\eqalign{ & = 125\% \,\,{\text{of}}\,\,{\text{Rs}}.x \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{125}}{{100}}x} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{5x}}{4} \cr} $$
Cost of monthly return ticket with extension :
$$\eqalign{ & = 105\% \,\,{\text{of}}\,\,{\text{Rs}}.\frac{{5x}}{4} \cr & = {\text{Rs}}{\text{. }}\left( {\frac{{105}}{{100}} \times \frac{{5x}}{4}} \right) \cr & = {\text{Rs}}{\text{. }}\frac{{21x}}{{16}} \cr} $$
$$\eqalign{ & \therefore \frac{{21x}}{{16}} = 84 \cr & \Rightarrow x = \left( {\frac{{84 \times 16}}{{21}}} \right) \cr & \Rightarrow x = 64 \cr} $$