From Delhi station if we buy 2 tickets to station A and 3 tickets to station B,the total cost is 77,  but if we buy tickets to station A and 5tickets to station B, the total cost is 124. What are the faresfrom Delhi to station A and to station B?.

Let the fares from Delhi to station A and to station B be x and y respectively.
Condition 1:
2 tickets to station A and 3 tickets to station B cost 77.
2x + 3y = 77 … (i)
Condition 2:
3 tickets to station A and 5 tickets to station B costs 124.
3x + 5y = 124 … (ii)
Multiplying (i) by 5 and (ii) by 3
5 (2x+3y = 77)
10x + 15y = 385 … (iii)
3 (3x+5y = 124)
9x + 15y = 372 … (iv)
Subtracting (iv) from (iii)
10x + 15y = 385
9x + 15y = 372
(-)     (-)     (-)
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x             = 13
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x = 13
Substitute x = 13 in (i)
2(13) + 3y = 77
26 + 3y = 77
3y = 77 - 26
3y = 51
y = 51/3
⇒ y = 17
. ^. . The cost of fare from Delhi to station A is 13.
And the cost of fare from Delhi to station B is 17.
Verification:
(a) 2x + 3y = 2(13) + 3 (17) = 26 + 51 = 77
(b) 3x + 5y = 3 (13) + 5 (17) = 39 + 85 = 124.