Directions: Read the table carefully and answer the following question. The…
2023
Directions: Read the table carefully and answer the following question.
The table shows data about the distance (km) covered from one point to another by the vehicle used between each pair of points, and the speed of each vehicle (km/hr). i.e., if a person wants to travel from one point to another, they can only use the vehicle available at the starting point.
Note: ** means there is no direct connection between the given points.
If Rahul travels from P to S via Q, and the fare per km of the vehicle from Q to S is 20% more than that from P to Q, then the total fare collected from P to S via Q is Rs. 72000. Find the fare of the taxi per km.
- A.
Rs. 100
- B.
Rs. 150
- C.
Rs. 120
- D.
Rs. 140
- E.
Rs. 130
Show answer & explanation
Correct answer: A
Concept
Total fare on a multi-leg journey = sum of (distance of each leg × fare-rate per km for the vehicle used on that leg). The vehicle on a leg is the one available at the leg's starting point. A rate that is “20% more” than a base rate r equals 1.2 × r. Form one linear equation in the unknown base rate and solve.
Application
Identify the legs of P → S via Q: leg 1 is P → Q and leg 2 is Q → S.
Read distances from the table: P → Q = 240 km and Q → S = 400 km.
Read vehicles from the starting points: at P the vehicle is the Taxi, at Q the vehicle is the Bus.
Let the taxi fare per km be x. The bus fare per km is 20% more, so it is 1.2x.
Set up the total-fare equation: 240·x + 400·(1.2x) = 72000.
Simplify: 240x + 480x = 720x, so 720x = 72000.
Solve: x = 72000 ÷ 720 = 100. The taxi fare per km is Rs. 100.
Cross-check
Plug back in: taxi leg = 240 × 100 = Rs. 24000; bus leg = 400 × 120 = Rs. 48000; total = 24000 + 48000 = Rs. 72000, which matches the given total. (The speed column is not needed here — it is data for other questions on the same table.)