Discussion
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 ?
Answer: B
The fares are Rs. 13 to B and Rs. 17 to C.
Let the fares be \(b\) and \(c\):
\[ \begin{aligned} 2b + 3c &= 77 \\ 3b + 2c &= 73 \\ 5b + 5c &= 150 \Rightarrow b + c = 30 \\ c - b &= 4 \end{aligned} \]
Subtracting the second equation from the first gives \(c - b = 4\), so \(c = 17\) and \(b = 13\). Check: \(2(13) + 3(17) = 77\) and \(3(13) + 2(17) = 73\). Rs. 17 and Rs. 13 swaps the two fares.
Adding and subtracting the two equations is the quickest way to solve a symmetric pair like this one.
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