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
(a)₹ 48
(b)₹ 64
(c)₹ 72
(d)₹ 80
Answer
Answer (as printed): B
Explanation
Let the cost of a single ticket be ₹ $x$. Then, cost of monthly return ticket $$=125 \% \text { of } ₹ x=₹\left(\frac{125}{100} x\right)=₹ \frac{5 x}{4} \text {. }$$ Cost of monthly return ticket with extension $$\begin{aligned} & =105 \% \text { of ₹ } \frac{5 x}{4}=₹\left(\frac{105}{100} \times \frac{5 x}{4}\right)=₹ \frac{21 x}{16} . \\ & \therefore \frac{21 x}{16}=84 \Rightarrow x=\left(\frac{84 \times 16}{21}\right)=64 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.