Anvita’s mobile company charges ₹2 for the first 5 minutes of a call, and 35 paise per minute after the first 5 minutes. If Anvita was charged ₹9 in total for a call with her friend, what was the duration (in minutes) of the call?
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Solving Mobile Call Duration Problem
This problem involves calculating the total duration of a mobile call based on a tiered pricing structure. We are given the cost for the initial duration and a different cost for subsequent minutes. We need to work backward from the total charge to find the total time spent on the call.
Understanding the Call Charging Structure
The mobile company charges in two parts:
- A fixed charge for the first 5 minutes.
- A per-minute charge for the time exceeding the initial 5 minutes.
Given Information
- Charge for the first 5 minutes: ₹2
- Charge per minute after the first 5 minutes: 35 paise
- Total charge for the call: ₹9
Step-by-Step Calculation of Call Duration
Step 1: Determine the cost for the duration after the first 5 minutes
The total charge includes the fixed cost for the first 5 minutes and the cost for the remaining time. We can find the cost for the remaining time by subtracting the initial fixed charge from the total charge.
Cost for time after first 5 minutes = Total Charge - Charge for first 5 minutes
Cost for time after first 5 minutes = \(₹9 - ₹2 = ₹7\)
Step 2: Convert the remaining cost to paise
The per-minute charge after the first 5 minutes is given in paise (35 paise), while the calculated cost for the remaining time is in Rupees (₹7). To find the number of minutes, we must use consistent units. We will convert Rupees to Paise, knowing that \(₹1 = 100\) paise.
Cost for time after first 5 minutes in Paise = \(₹7 \times 100\) paise/₹
Cost for time after first 5 minutes in Paise = \(700\) paise
Step 3: Calculate the duration after the first 5 minutes
Now we know the total cost for the time after the first 5 minutes (700 paise) and the charge per minute for this period (35 paise). We can find the number of minutes by dividing the total cost by the per-minute rate.
Duration after first 5 minutes = Total Cost after first 5 minutes / Charge per minute after first 5 minutes
Duration after first 5 minutes = \(700\) paise / \(35\) paise/minute
Duration after first 5 minutes = \(20\) minutes
Step 4: Calculate the total duration of the call
The total duration of the call is the sum of the initial 5 minutes and the duration calculated in Step 3.
Total Duration = Duration of first 5 minutes + Duration after first 5 minutes
Total Duration = \(5\) minutes + \(20\) minutes
Total Duration = \(25\) minutes
Summary of Calculations
| Item | Value |
|---|---|
| Charge for first 5 minutes | ₹2 |
| Total Charge | ₹9 |
| Cost for duration after first 5 minutes (₹) | \(₹9 - ₹2 = ₹7\) |
| Cost for duration after first 5 minutes (paise) | \(₹7 \times 100 = 700\) paise |
| Charge per minute after first 5 minutes | 35 paise |
| Duration after first 5 minutes | \(700 \div 35 = 20\) minutes |
| Total Duration of Call | \(5 + 20 = 25\) minutes |
Therefore, the total duration of Anvita's call was 25 minutes.
Revision Table: Mobile Call Pricing
| Concept | Description | Formula Example |
|---|---|---|
| Tiered Pricing | Different rates applied to different parts of usage (e.g., first X units at one rate, subsequent units at another). | Total Cost = (Cost for Tier 1) + (Cost for Tier 2) + ... |
| Unit Conversion | Converting between different units of the same type (e.g., Rupees to Paise, minutes to seconds). | \(1\) Rupee = \(100\) Paise |
| Calculating Duration from Cost | If total cost and per-unit rate are known, duration = Total Cost / Rate per Unit. | Minutes = Total Paise / Paise per Minute |
Additional Information: Solving Word Problems
When approaching word problems like this mobile call duration calculation, it's helpful to follow these steps:
- Read Carefully: Understand all the information given and what is being asked. Identify key numbers and rates.
- Identify the Structure: Determine how the calculation works (e.g., fixed cost + variable cost, different rates for different periods).
- Break It Down: Separate the problem into smaller, manageable steps. For example, first calculate the cost for a part, then use that cost to find a duration.
- Check Units: Ensure all values used in a calculation have the same units (e.g., all in Rupees or all in Paise, all in minutes or all in hours). Convert units if necessary.
- Perform Calculations: Do the arithmetic carefully.
- Check Your Answer: Does the calculated answer make sense in the context of the problem? You can test the answer by calculating the total cost for your found duration to see if it matches the given total cost.
By applying these steps, you can systematically solve problems involving different rates and durations.
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