Mr .sharma and Mr Arora are family friends and they decided to go for a trip with family.for the trip,they reserved their rail tickets .Mr. Arora has not taken a half ticket for his child who is 6years old, whereas Mr sharma has taken half tickets for his two children ,who are 6.5years and 8 years old.A railway half ticket costs half of the full fare but the reservation charges are the same as on a full ticket .Mr and Mrs Arora paid Rs 1700,while Mr and Mrs sharma paid Rs 2700 ,sharma paid Rs 2700. find the full fare of one ticket and the reservarion charges per ticket.l will mark the answer as brainliest .plz solv this question.
Answers
Answer:
Step-by-step explanation:
Let the railway full fare of one ticket for a trip be RS 'x' so,, half fare will be RS x/2
Le the reservation charges be RS y
A.T.Q
x+y+x+y=1700
2x+2y=1700-----------(1)
x+y+x+y+x/2+x/2=2700
3x+4y=2700---------(2)
Multiple (1)by 2
We get, 4x+4y=3400---------(3)
Subtract (2)from (3)
(4x+4y)-(3x+4y)=3400-2700
X=700
Subtitute X=700 in (1)
1400+2y=1700
2y=1700-1400
2y=300
y=150
The full fare of one ticket is Rs 700 and the reservation charges per ticket is Rs 300.
Let's assume the full fare of one ticket to be x and the reservation charges to be y.
Since Mr Arora did not take a half ticket for his child, the total cost of their tickets would be (2x + y) since they would have paid for a full ticket for their child. However, since Mr and Mrs Arora paid Rs 1700 in total, we can write the equation:
2x + y = 1700 ----(1)
On the other hand, Mr Sharma has taken half tickets for his two children, so the total cost of their tickets would be (x + 0.5x + y) = 1.5x + y. Therefore, the total cost paid by Mr and Mrs Sharma can be written as:
2(1.5x + y) = 3x + 2y = 2700 ----(2)
Now we have two equations (1) and (2) with two unknowns, which we can solve simultaneously. We can start by simplifying equation (2):
3x + 2y = 2700
=> 6x + 4y = 5400 (multiplying both sides by 2)
Now we can eliminate y by subtracting equation (1) from equation (2):
(6x + 4y) - (2x + y) = 5400 - 1700
=> 4x + 3y = 3700
We now have two equations:
2x + y = 1700
4x + 3y = 3700
Multiplying the first equation by 3 and subtracting it from the second equation, we get:
4x + 3y - (6x + 3y) = 3700 - 5100
=> -2x = -1400
=> x = 700
Substituting the value of x in equation (1), we get:
2x + y = 1700
=> 2(700) + y = 1700
=> y = 300
Therefore, the full fare of one ticket is Rs 700 and the reservation charges per ticket is Rs 300.
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