Select the correct answerTwo 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 ?Options Rs. 13, Rs. 17Rs. 4, Rs. 23 Rs. 15, Rs. 14 Rs. 17, Rs. 13
Question
Select the correct answerTwo 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 ?Options Rs. 13, Rs. 17Rs. 4, Rs. 23 Rs. 15, Rs. 14 Rs. 17, Rs. 13
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 the following two equations:
2x + 3y = 77 (equation 1)
3x + 2y = 73 (equation 2)
We can solve these equations simultaneously to find the values of x and y.
First, multiply equation 1 by 3 and equation 2 by 2:
6x + 9y = 231
6x + 4y = 146
Subtract the second equation from the first:
5y = 85
So, y = 85 / 5 = Rs. 17
Substitute y = 17 into equation 1:
2x + 3*17 = 77
2x + 51 = 77
2x = 77 - 51 = 26
So, x = 26 / 2 = Rs. 13
Therefore, the fare for city B from A is Rs. 13 and the fare for city C from A is Rs. 17.
So, the correct answer is Rs. 13, Rs. 17.
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