Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77, but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A?

Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77, but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A? Correct Answer Rs. 13. Rs. 17

Given:

2 bus tickets from city A to B + 3 bus tickets from city A to C cost Rs.77

3 bus tickets from city A to B + 2 bus tickets from city A to C cost Rs.73

Calculation:

Let the price of a bus ticket from city A to B be Rs.x

And the price of a bus ticket from city A to C be Rs.y

⇒ 2x + 3y = 77      ------(1)  

And,

⇒ 3x + 2y = 73      ------(2)

Now solve the simultaneous equations,

Multiplying 1st equation by 2 and 2nd equation by 3,

⇒ 4x + 6y = 154      ------(3)  

And

⇒ 9x + 6y = 219      ------(4)

Subtracting equation 3 from equation 4,

⇒ (9x + 6y) - (4x + 6y) = 219 - 154

⇒ 9x + 6y - 4x - 6y = 65

⇒ 5x = 65

⇒ x = 65\5

⇒ x = 13

Using the above value of x in 1st equation,

⇒ 2x + 3y = 77

⇒ 2(13) + 3y = 77

⇒ 26 + 3y = 77

⇒ 3y = 77 – 26

⇒ 3y = 51

⇒ y = 51/3

⇒ y = 17

∴ The price of a bus ticket from city A to B is Rs.13

And,

The price of a bus ticket from city A to C is Rs.17