Mathematics
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 ₹ 315 and for a journey of 15 km, the charge paid is ₹ 465. What are the fixed charges and the charge per kilometer ? How much does a person have to pay for travelling a distance of 32 km ?
Linear Equations
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Answer
Let fixed charge be ₹ x and charge per kilometer be ₹ y.
Given,
For a distance of 10 km, the charge paid is ₹ 315.
⇒ x + 10y = 315 ……..(1)
For a distance of 15 km, the charge paid is ₹ 465.
⇒ x + 15y = 465 ……..(2)
Subtracting equation (1) from (2), we get :
⇒ (x + 15y) - (x + 10y) = 465 - 315
⇒ x - x + 15y - 10y = 150
⇒ 5y = 150
⇒ y = = ₹ 30.
Substituting value of y in equation (1), we get :
⇒ x + 10 × 30 = 315
⇒ x + 300 = 315
⇒ x = 315 - 300 = ₹ 15.
For 32 km,
Charge = x + 32y = 15 + 32 × 30
= 15 + 960 = ₹ 975.
Hence, fixed charge = ₹ 15m, charge per kilometer = ₹ 30 and for 32 km charge = ₹ 975.
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