A monthly return railway ticket costs 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 ₹ 84, the price of the single ticket is

Concept & Logic Express all costs in terms of a single variable, forming a linear equation based on cumulative percentage increases. Step-by-Step Solution * Let the price of a single ticket be $x$. * Cost of a monthly return ticket = $x + 25\%$ of $x = 1.25x$. * Cost of a week's extension = $5\%$ of the monthly ticket cost = $0.05 \times 1.25x = 0.0625x$. * Total cost with extension = $1.25x + 0.0625x = 1.3125x$. * We are given this total cost is ₹ $84$. * Equation: $1.3125x = 84 \Rightarrow \frac{21}{16}x = 84 \Rightarrow x = \frac{84 \times 16}{21} = 64$. Exam Strategy & Shortcut Work with fractions for faster computation: Monthly ticket is $\frac{5}{4}$ of single. Extension is $\frac{1}{20}$ of Monthly. Total = $\frac{5}{4} + (\frac{1}{20} \times \frac{5}{4}) = \frac{5}{4} + \frac{1}{16} = \frac{21}{16}$. Now, $\frac{21}{16}$ of Single = $84$. Single = $84 \times \frac{16}{21} = 64$. Common Pitfall Calculating the $5\%$ extension fee on the single ticket price instead of the monthly ticket price. Read carefully to identify the correct base value for each percentage. Final Answer Therefore, the correct answer is **₹ 64**.