In certain city the Taxi charges comprise of a fixed charge and the charge of…
2013
In certain city the Taxi charges comprise of a fixed charge and the charge of the distance travelled. A person paid ₹ 156 for a journey of 16 km and another person paid ₹ 204 for the journey of 24 km. The amount paid by a passenger who has travelled 30 km is
Answer: B. 240 — ConceptA fare formed by a fixed charge and a constant rate per kilometre is a linear model: T(d) = F + rd. Two fare observations give two linear equations;…
- A.
236
- B.
240
- C.
248
- D.
256
Show answer & explanation
Correct answer: B
Concept
A fare formed by a fixed charge and a constant rate per kilometre is a linear model: T(d) = F + rd.
Two fare observations give two linear equations; subtracting them eliminates the fixed charge and reveals the rate per kilometre.
Application
Let F be the fixed charge and r be the charge per kilometre.
From the two journeys, 156 = F + 16r and 204 = F + 24r.
Subtract the first equation from the second: 204 − 156 = (F + 24r) − (F + 16r), so 48 = 8r and r = 6.
Substitute r = 6 into the first equation: F = 156 − 16 × 6 = 60.
For 30 km, T(30) = 60 + 30 × 6 = 240.
Cross-check
With F = 60 and r = 6, the fares for 16 km and 24 km are ₹156 and ₹204 respectively, matching both observations. Therefore, the amount for 30 km is ₹240.