Two bus tickets from city Amb to Sunhet and three tickets from city Amb to…
2023
Two bus tickets from city Amb to Sunhet and three tickets from city Amb to Dehra cost Rs. 77 but three tickets from city Amb to Sunhet and two tickets from city Amb to Dehra cost Rs. 73. What are the fares for cities Sunhet and Dehra from Amb?
- A.
Rs. 4, Rs. 23
- B.
Rs. 13, Rs. 17
- C.
Rs. 15, Rs. 14
- D.
Rs. 17, Rs. 13
Show answer & explanation
Correct answer: B
Concept: A word problem that gives two different ticket combinations of the same two unknown fares is a system of two linear equations in two variables. Such a system, when the two equations are independent, has a unique solution — found by scaling the equations so one variable's coefficient matches in both, subtracting to eliminate that variable, solving for the other, and then back-substituting.
Application: Let Rs. x be the fare from Amb to Sunhet and Rs. y be the fare from Amb to Dehra. The two ticket combinations give:
2x + 3y = 77 ... (i)
3x + 2y = 73 ... (ii)
Multiply equation (i) by 3: 6x + 9y = 231.
Multiply equation (ii) by 2: 6x + 4y = 146.
Subtract the second result from the first to eliminate x: 5y = 85, so y = 17.
Substitute y = 17 into equation (i): 2x + 3(17) = 77, so 2x = 26, giving x = 13.
Cross-check: Substitute x = 13 and y = 17 into equation (ii): 3(13) + 2(17) = 39 + 34 = 73, which matches the given total. Both equations are satisfied, confirming the fare from Amb to Sunhet is Rs. 13 and the fare from Amb to Dehra is Rs. 17.