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Question

From Dharmapuri bus stand if we buy 2 tickets to Palacode and 3 tickets to Karimangalam the total cost is Rs.32, but if we buy 3 tickets to Palacode and one ticket to Karimangalam the total cost is Rs. 27. Find the fares from Dharmapuri to Palacode and to Karimangalam.

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Solution

Let the fare from Dharmpuri to Palacode be Rs. x and to Karimangalam be Rs. y.

From the given data, we have

2x+3y=32 ......... (1)

3x+y=27 ......... (2)

Equation (2) becomes, y=27−3x (3)

Substituting y in (1) we get, 2x+3(27−3x)=32

⇒2x+81−9x=32

2x−9x=32−81

−7x=−49

∴x=−49−7=7

Substituting x = 7 in (3) we get, y=27−3(7)=27−21=6

∴ The fare from Dharmapuri to Palacode is Rs. 7 and to Karimangalam is Rs. 6.

From the given data, we have

2x+3y=32 ......... (1)

3x+y=27 ......... (2)

Equation (2) becomes, y=27−3x (3)

Substituting y in (1) we get, 2x+3(27−3x)=32

⇒2x+81−9x=32

2x−9x=32−81

−7x=−49

∴x=−49−7=7

Substituting x = 7 in (3) we get, y=27−3(7)=27−21=6

∴ The fare from Dharmapuri to Palacode is Rs. 7 and to Karimangalam is Rs. 6.

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