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 ?
Question
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 ?
Solution
Let's denote the cost of a ticket from city A to B as 'x' and the cost of a ticket from city A to C as 'y'.
From the problem, we have two equations:
- 2x + 3y = 77
- 3x + 2y = 73
We can solve these equations step by step:
First, multiply the first equation by 3 and the second equation by 2:
- 6x + 9y = 231
- 6x + 4y = 146
Subtract the second equation from the first:
5y = 85
So, y = 85 / 5 = 17. This means that the fare from city A to C is Rs. 17.
Substitute y = 17 into the first equation:
2x + 3*17 = 77 2x + 51 = 77 2x = 77 - 51 2x = 26 x = 26 / 2 = 13
So, the fare from city A to B is Rs. 13.
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