Two railway tickets from city A to B and three tickets from city A to C cost ₹…

Concept: A pair of linear equations in two unknowns can be solved by the elimination method — multiply each equation by a suitable constant so that one variable has the same coefficient in both equations, then subtract (or add) the equations to eliminate that variable and solve for the other.

Let x be the fare (in ₹) for one ticket from city A to city B, and y be the fare (in ₹) for one ticket from city A to city C.

1. Write the two given cost relations as equations: 2x + 3y = 177 ...(i) and 3x + 2y = 173 ...(ii).

2. Multiply equation (i) by 3 and equation (ii) by 2 so that the coefficient of x becomes 6 in both: 6x + 9y = 531 ...(iii) and 6x + 4y = 346 ...(iv).

3. Subtract equation (iv) from equation (iii) to eliminate x: 5y = 185, so y = 37.

4. Substitute y = 37 into equation (i): 2x + 3(37) = 177, so 2x + 111 = 177, so 2x = 66, so x = 33.

Cross-check: substituting x = 33 and y = 37 into equation (ii) gives 3(33) + 2(37) = 99 + 74 = 173, which matches the given total, confirming the values.

So the fare for city B from city A is ₹ 33.