The charges for a five-day trip by a tourist bus for one full ticket and a half-ticket are Rs. 1440 inclusive of boarding charges which are same for a full ticket and a half-ticket. The charges for the same trip for 2 full tickets and one half-ticket inclusive of boarding charges are Rs. 2220. The fare for a half-ticket is 75% of the full ticket. Find the fare and the boarding charges separately for one full ticket.
Correct Answer: Rs. 480, Rs. 300
Let the fare for a full ticket be Rs. x and the boarding charges be Rs. y per ticket.
Then, fare for a half-ticket :
= 75% of Rs. x = Rs. $$\frac{3x}{4}$$
$$\eqalign{ & \therefore \left( {x + y} \right) + \left( {\frac{3}{4}x + y} \right) = 1440 \cr & \Rightarrow \frac{{7x}}{4} + 2y = 1440 \cr & \Rightarrow 7x + 8y = 5760 ..... (i) \cr & {\text{And, 2}}\left( {x + y} \right) + \left( {\frac{3}{4}x + y} \right) = 2220 \cr & \Rightarrow \frac{{11x}}{4} + 3y = 2220 \cr & \Rightarrow 11x + 12y = 8880 ..... (ii) \cr} $$
Solving (i) and (ii), we have, x = 480, y = 300
Then, fare for a half-ticket :
= 75% of Rs. x = Rs. $$\frac{3x}{4}$$
$$\eqalign{ & \therefore \left( {x + y} \right) + \left( {\frac{3}{4}x + y} \right) = 1440 \cr & \Rightarrow \frac{{7x}}{4} + 2y = 1440 \cr & \Rightarrow 7x + 8y = 5760 ..... (i) \cr & {\text{And, 2}}\left( {x + y} \right) + \left( {\frac{3}{4}x + y} \right) = 2220 \cr & \Rightarrow \frac{{11x}}{4} + 3y = 2220 \cr & \Rightarrow 11x + 12y = 8880 ..... (ii) \cr} $$
Solving (i) and (ii), we have, x = 480, y = 300