Question

# From Delhi station, if we buy 2 tickets for station A and 3 tickets for station B, the total cost is Rs. 77. But if we buy 3 tickets for station A and 5 tickets for station B, the total cost is Rs. 124. What are the fares from Delhi to station A and to station B?

A
A=Rs.12;B=Rs.17
B
A=Rs.13;B=Rs.17
C
A=Rs.18;B=Rs.17
D
A=Rs.19;B=Rs.17

Solution

## The correct option is B $$A = Rs. 13 ; B = Rs. 17$$Let the cost of ticket to station $$A$$ be Rs $$x$$ and to station $$B$$ be Rs $$y$$.Given that, "if we buy $$2$$ tickets for station $$A$$ and $$3$$ tickets for station $$B$$, the total cost is $$Rs.\ 77$$." $$\Rightarrow 2x + 3y = 77$$ --- (1)Also, "if we buy $$3$$ tickets for station $$A$$ and $$5$$ tickets for station $$B$$, the total cost is $$Rs.\ 124$$." $$\Rightarrow 3x + 5y = 124$$ --- (2)Multiplying equation  $$(1)$$ by $$3$$, we get, $$6x + 9y = 231$$ ----- equation $$(3)$$Multiplying equation  $$(2)$$ by $$2$$, we get, $$6x + 10y = 248$$ ----- equation $$(4)$$Subtracting equation $$(3)$$ from $$(4)$$, we get:$$(6x+10y)-(6x+9y)=248-231$$$$\Rightarrow y = 17$$ Substituting $$y = 17$$ in the equation $$(1)$$, we get: $$2x + 3(17) = 77$$$$\Rightarrow x = 13$$Hence, the fare from Delhi to station $$A$$ is $$Rs.\ 13$$ and to station $$B$$ is $$Rs.\ 17$$.Mathematics

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