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

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."

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)=248231

y=17

Substituting y=17 in the equation (1), we get:

2x+3(17)=77

x=13

Hence, the fare from Delhi to station A is Rs. 13 and to station B is Rs. 17.


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