From Delhi station, if we buy 2 tickets for station A and 3 tickets for station B, the total cost is ₹ 77. But if we buy 3 tickets for station A and 5 tickets for station B, the total cost is ₹ 124. What are the fares from Delhi to station A and to station B ?

Let cost of ticket from Delhi to station A be ₹ x and cost of ticket from Delhi to station B be ₹ y.

Given,

From Delhi station, if we buy 2 tickets for station A and 3 tickets for station B, the total cost is ₹ 77.

⇒ 2x + 3y = 77 …….(1)

Given,

From Delhi station, if we buy 3 tickets for station A and 5 tickets for station B, the total cost is ₹ 124.

⇒ 3x + 5y = 124 …….(2)

Multiplying equation (1) by 3, we get :

⇒ 3(2x + 3y) = 3 × 77

⇒ 6x + 9y = 231 …….(3)

Multiplying equation (2) by 2, we get :

⇒ 2(3x + 5y) = 2 × 124

⇒ 6x + 10y = 248 …….(4)

Subtracting equation (3) from (4), we get :

⇒ (6x + 10y) - (6x + 9y) = 248 - 231

⇒ 6x - 6x + 10y - 9y = 17

⇒ y = ₹ 17.

Substituting value of y in equation (1), we get :

⇒ 2x + 3(17) = 77

⇒ 2x + 51 = 77

⇒ 2x = 77 - 51

⇒ 2x = 26

⇒ x = $\dfrac{26}{2}$ = ₹ 13.

Hence, fares from Delhi to station A = ₹ 13 and to station B = ₹ 17.