The taxi charges in a city consist of a fixed charge together with the charge per kilometre for the distance covered. For a distance of 35 km, the charge paid is ₹375 and for a distance of 48 km, the charge paid is ₹427. Find the fixed charges and the charge per km (in ₹), respectively.
235 and 4
To solve the problem of finding the fixed charges and charge per kilometer for a taxi service, consider the following:
- Let the fixed charge be denoted as F (in ₹).
- Let the charge per kilometer be k (in ₹).
The charges for a given trip can be represented by the equation:
Charge = F + (Distance × k)
We are given two scenarios:
- For a distance of 35 km, the total charge is ₹375:
375 = F + 35k - For a distance of 48 km, the total charge is ₹427:
427 = F + 48k
We now have two equations:
- F + 35k = 375
- F + 48k = 427
We can solve these equations simultaneously to find the values of F and k:
Subtract equation (1) from equation (2):
(F + 48k) - (F + 35k) = 427 - 375
48k - 35k = 52
13k = 52
k = 52/13 => k = 4
Now, substitute the value of k back into equation (1):
F + 35(4) = 375
F + 140 = 375
F = 375 - 140
F = 235
Thus, the fixed charge is ₹235 and the charge per kilometer is ₹4.
The correct answer is: 235 and 4.
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