A railway half-ticket costs half the full ticket. However, the reservation charge for all the tickets is constant. One full reserved ticket for a journey is ₹525. If the cost of one full and one half reserved ticket for the same journey is ₹850, then what is the reservation charge per ticket?

Question

Accepted Answer

Let $$ x $$ be the fare of a full ticket and $$ y $$ be the reservation charge.

From the problem:  
1. The total cost of one full reserved ticket is:  
   $$
   x + y = 525 	ag{1}
   $$

2. The cost of one full reserved ticket and one half reserved ticket is:  
   $$
   x + y + \frac{x}{2} + y = 850
   $$  
   Simplify:  
   $$
   \frac{3x}{2} + 2y = 850
   $$  
   Multiply through by 2 to eliminate fractions:  
   $$
   3x + 4y = 1700 	ag{2}
   $$

Solve equations (1) and (2):  
From (1):  
$$
x + y = 525 \implies x = 525 - y
$$

Substitute $$ x = 525 - y $$ into (2):  
$$
3(525 - y) + 4y = 1700
$$  
$$
1575 - 3y + 4y = 1700
$$  
$$
1575 + y = 1700
$$  
$$
y = 125
$$

Thus, the reservation charge per ticket is **₹125**.

Answer

Answer

Answer