Math Problem Statement

Monish travelled to New Delhi and hired a taxi there. The taxi charges were as follows: i) Rs 500 for 4 hours. ii) Additional charges for extra hours @ Rs 50 per hour. iii) Additional charges for distance over 100 km @ Rs 20 per km. He hired the taxi from 8 am to 2 pm and travelled 120 kms. How much did he pay for hiring the taxi?

Solution

To solve the problem, let's break it down step-by-step.

Given Information:

  1. Rs 500 for 4 hours.
  2. Additional charges for extra hours: Rs 50 per hour.
  3. Additional charges for distance over 100 km: Rs 20 per km.

Monish's taxi ride:

  • He hired the taxi from 8 am to 2 pm (a total of 6 hours).
  • He travelled 120 km.

Step 1: Basic charges for 4 hours

The base charge for the first 4 hours is Rs 500.

Step 2: Extra hours charge

He hired the taxi for 6 hours, so he used 2 extra hours.

  • Additional charge for 2 extra hours = 2 × Rs 50 = Rs 100.

Step 3: Distance charge

He travelled 120 km, and the base charge covers up to 100 km. So, the extra distance travelled is:

  • Extra distance = 120 km - 100 km = 20 km.
  • Charge for extra distance = 20 km × Rs 20 = Rs 400.

Total cost:

  • Base charge = Rs 500
  • Additional charges for extra hours = Rs 100
  • Additional charges for distance = Rs 400

So, total cost = Rs 500 + Rs 100 + Rs 400 = Rs 1000.

Final Answer:

The total amount Monish paid for the taxi is Rs 1000. The correct answer is C.

Let me know if you would like a detailed explanation or have any questions!

Here are some additional related questions to further understand the topic:

  1. How do you calculate the total cost of a taxi ride if there are multiple time and distance-based charges?
  2. What is the formula to calculate the extra charge for time if the base time is exceeded?
  3. How can we calculate the charge for extra distance traveled if the first 100 km are free?
  4. How would the final cost change if the extra hours charge was Rs 60 instead of Rs 50?
  5. What is the significance of the base charge in this problem?

Tip: When calculating costs with varying charges, break the problem into smaller steps (time charges and distance charges), and handle them separately to avoid confusion.

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Math Problem Analysis

Mathematical Concepts

Arithmetic
Time and Distance
Unit Rate

Formulas

Base cost = Fixed cost for 4 hours
Extra hour cost = (Total hours - 4) * Cost per extra hour
Extra distance cost = (Total distance - 100 km) * Cost per km for extra distance
Total cost = Base cost + Extra hour cost + Extra distance cost

Theorems

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Suitable Grade Level

Grade 8