Math Problem Statement
Solution
To solve the problem, let's break it down step-by-step.
Given Information:
- Rs 500 for 4 hours.
- Additional charges for extra hours: Rs 50 per hour.
- 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:
- How do you calculate the total cost of a taxi ride if there are multiple time and distance-based charges?
- What is the formula to calculate the extra charge for time if the base time is exceeded?
- How can we calculate the charge for extra distance traveled if the first 100 km are free?
- How would the final cost change if the extra hours charge was Rs 60 instead of Rs 50?
- 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