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 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?

Answer 1

Answer:

your answer hope it help you

Step-by-step explanation:

Let cost of ticket to station A be Rs x and to station B be Rs y.

As per the statement, "if we buy 2 ticket for station A and 3 tickets for station B, the total cost is Rs. 77." =>2x+3y=77 --- (1)

And, as per Ajay "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) with 3 we get, 6x+9y=231 ----- equation (3)

Multiplying equation (2) with 2 we get, 6x+10y=248 ----- equation (4)

Subtracting equation (3)

from (4), we get y=17

Substituting y=17 in the

equation (1), we get 2x+3(17)=77=>x=13

Hence, cost of ticket to A is Rs 13 and to B is Rs 17

Answer 2

Let the cost of tickets A be x and B be y.

1st Case

• Number of Tickets for station A = 2

• Number of Tickets for station B = 3

2nd Case

• Number of Tickets for station A = 3

• Number of Tickets for station B = 5

Given Situation

• If we buy 2 Tickets for station A and 3 Tickets for station B . The total cost Rs.77

${\sf\footnotesize~~~~~★~~\implies~~ 2x + 3y = 77 \: \: \: \: \: - - - - (1)}$

• If we buy 3 Tickets for station A and 5 Tickets for station B . The total cost Rs.124.

${\sf\footnotesize~~~~~★~~\implies~~ 3x + 5y = 124 \: \: \: \: \: - - - - (4)}$

• On Solving Equation (1)

${\sf\footnotesize~~~~~~~\implies~~ 2x + 3y = 77 }$

${\sf\footnotesize~~~~~~~\implies~~ 2x = 77 - 3y }$

${\sf\footnotesize~~~~~~~\implies~~ x = \dfrac{ 77 - 3y}{2} }$

• Putting the value of x in Equation (2)

${\sf\footnotesize~~~~~~~\implies~~ 3 \bigg( \dfrac{ 77 - 3y}{2} \bigg) + 5y = 124 }$

${\sf\footnotesize~~~~~~~\implies~~ \dfrac{ 231 - 9y}{2} + 5y = 124 }$

${\sf\footnotesize~~~~~~~\implies~~ \dfrac{ 231 - 9y + 10y }{2}= 124 }$

${\sf\footnotesize~~~~~~~\implies~~ 231 + y= 124 \times 2 }$

${\sf\footnotesize~~~~~~~\implies~~ y= 248 - 231}$

${\sf\footnotesize~~~~~~~\implies~~ y= 17}$

• Putting the value of y in Equation (1)

${\sf\footnotesize~~~~~~~\implies~~ 2x + 3(17) = 77 }$

${\sf\footnotesize~~~~~~~\implies~~ 2x + 51= 77 }$

${\sf\footnotesize~~~~~~~\implies~~ 2x = 77 - 51 }$

${\sf\footnotesize~~~~~~~\implies~~ 2x = 26 }$

${\sf\footnotesize~~~~~~~\implies~~ x = 13 }$

• Hence, cost of ticket to A is Rs 13 and to B is Rs 17.