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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.

A. Rs. 580, Rs. 400

B. Rs. 280, Rs. 200

C. Rs. 480, Rs. 300

D. Rs. 380, Rs. 400

Answer: Option C

Solution(By Examveda Team)

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

This Question Belongs to Arithmetic Ability >> Percentage

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