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 Delhi to station $$A$$ and to station $$B$$.

Solution

## Let, the fare of ticket for station $$A$$ be Rs. $$x$$and the fare of ticket for station $$B$$ be Rs.$$y$$$$2x+3y=77.....(1)$$and$$3x+5y=124.....(2)$$Multiplying equation no. (1) by $$3$$ and (2) by $$2$$.$$6x+9y=231.....(3)$$$$6x+10y=248.....(4)$$.$$- - -$$______________$$-y=-17$$$$y=17$$From $$(1)2x+3(17)=77$$$$2x=77-51$$$$2x=36$$$$x=13$$Thus, fare for station $$A$$=Rs. $$13$$and, fare for station $$B$$=Rs. $$17$$.Mathematics

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