The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs 105 and for a journey of 15 km, the charge paid is Rs 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
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Question
The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is Rs. 105 and for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per kilometer? How much does a person have to pay for travelling a distance of 25 km?
Solution
Let the fixed charge be x
& the variable charge be y.
Given that charge paid for 10 km is Rs 105 and for 15 km is Rs 155
So,
Fixed charge +
10
×
(Charge per km)
=
R
s
105
x
+
10
y
=
105
⇒
x
=
105
−
10
y
(1)
And for 15 kilometers,
x
+
15
y
=
155
⇒
x
=
155
−
15
y
(2)
From (1) and (2)
105
−
10
y
=
155
−
15
y
⇒
y
=
10
putting value of y in equation (1)
x
=
105
−
10
×
10
x
=
5
For travelling 25 km, he has to pay
=
x
+
25
y
(5 + 25
×
10)
= Rs.255.
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