Question

From Jalandhar, if we buy 3 tickets for station X and 4 tickets for station Y the total cost is 80rs. But if we buy 2 tickets for station X and 6 tickets for station Y then the total cost is 100rs. What are the fares from Jalandhar to station X and station Y.

Answer 1

Hint: According to given in the question from Jalandhar, if we buy 3 tickets for station X and 4 tickets for station Y the total cost is 80r and if we buy 2 tickets for station X and 6 tickets for station Y then the total cost is 100rs hence, to find the fares from Jalandhar to station X and station Y we have to let the fares for station X and station Y.
This logic gives us two variable linear equations.
Now, to find the values as we let in the beginning which are the fares from Jalandhar to station X and station Y we have to solve both of the obtained linear equations by sublimation method.

Complete step by step answer:
Given,
If we buy 3 tickets for station X and 4 tickets for station Y the total cost is 80rs and,
If we buy 2 tickets for station X and 6 tickets for station Y then total cost is 100rs
Step 1: First of all we have to let the fare from Jalandhar to station $X$ is $ a$, and similarly the fare from Jalandhar to station $Y$ is $b$.
Step 2: As given in the question, if we buy 3 tickets for station X and 4 tickets for station Y the total cost is 80rs.
Hence, we can form a linear equation with two variables as given below:
$3a + 4b = 80.........................(1)$
Step 3: As given in the question, if we buy 2 tickets for station X and 6 tickets for station Y the total cost is 100rs.
Hence, we can form a linear equation with two variables as given below:
$2a + 6b = 100.......................(2)$
Step 4: Now, to find the values of a, and b we have to solve both of the linear equations (1) and (2). To solve the both of the equations first of all we will divide by 2 both of the terms of the equation (2). Hence,
$a + 3b = 50........................(3)$
Now, on multiplying with 3 both of the terms of the equation (3)
$3a + 9b = 150..........................(4)$
Step 5: Now, to find the values of a, and b we have to solve the obtained equations(1) and (4) by subtracting both of the linear equations.
Hence,
$
\Rightarrow (3a + 4b) - (3a + 9b) = 80 - 150 \\
\Rightarrow 3a + 4b - 3a - 9b = - 70 \\
 $
On, eliminating term 3a from the obtained equation.
$
\Rightarrow - 5b = - 70 \\
\Rightarrow b = \dfrac{{70}}{5} \\
\Rightarrow b = 14 \\
 $
Hence, Fare from Jalandhar to station Y is 14rs
Step 6: On substituting the value of b in equation (1) we can obtain the value of a.
$
\Rightarrow 3a + 4(14) = 80 \\
\Rightarrow 3a = 80 - 56 \\
\Rightarrow a = \dfrac{{24}}{3} \\
\Rightarrow a = 8 \\
 $
Hence, Fare from Jalandhar to station X is 8rs

On solving the both of the linear equations with two variables we have obtained the Fare from Jalandhar to stations X, and Y are 8rs and 14rs.

Note:
To obtain the linear equations with two variables it is necessary to let the fares.
To solve the obtained linear equations with variables a, and b we have to solve both of the equations with the help of sublimation method.
First solve the linear equation for b in terms of a. Then substitute that expression for b in the other linear equation and we will get the equation in form of a.