If the cost of 157 litre of oil is Rs. 29763.65, then what is the cost per litre (rounded off to two decimal places)?
Understanding the Oil Cost Problem
The question asks us to find the cost of a single litre of oil when we are given the total cost for a larger quantity (157 litres). This is a common type of problem where we need to find the unit price or cost per unit.
Given Information
We are provided with the following details:
- Total quantity of oil: 157 litres
- Total cost of 157 litres of oil: Rs. 29763.65
Goal: Calculate Cost Per Litre
Our objective is to determine the cost of 1 litre of oil. To find the cost per litre, we need to divide the total cost by the total number of litres.
The formula for calculating the cost per litre is:
$$\text{Cost per litre} = \frac{\text{Total Cost}}{\text{Total Quantity in Litres}}$$
Step-by-Step Cost Calculation
Let's plug in the given values into the formula:
$$\text{Cost per litre} = \frac{\text{Rs. } 29763.65}{\text{157 litres}}$$
Now, we perform the division:
$$\frac{29763.65}{157} \approx 189.57738$$
The result of the division is approximately 189.57738.
Rounding Off to Two Decimal Places
The question specifically asks to round off the cost per litre to two decimal places. To do this, we look at the third decimal place.
- Our calculated value is 189.57738...
- The third decimal place is 7.
- Since 7 is 5 or greater, we round up the second decimal place.
- The second decimal place is 7, so rounding it up gives 8.
Therefore, rounding 189.57738 to two decimal places gives us 189.58.
Final Cost Per Litre
After performing the division and rounding, the cost per litre of oil is Rs. 189.58.
Summary of Solution Steps
Here is a summary of the steps taken to find the cost per litre:
| Step | Description | Calculation |
|---|---|---|
| 1 | Identify Total Cost and Quantity | Total Cost = Rs. 29763.65, Quantity = 157 litres |
| 2 | Divide Total Cost by Quantity | $\frac{29763.65}{157}$ |
| 3 | Perform Division | $\approx 189.57738$ |
| 4 | Round to Two Decimal Places | Round 189.57738 to 189.58 |
| 5 | State Final Cost per Litre | Rs. 189.58 |
Revision Table: Key Concepts
Review these key concepts related to solving unit price problems:
| Concept | Explanation | Application in Problem |
|---|---|---|
| Unit Price | The cost of one single item or unit (like 1 litre, 1 kg, 1 item). | We are finding the cost per 1 litre. |
| Division | The mathematical operation used to share a total amount equally among a number of groups or units. | Used to divide the total cost by the total number of litres. |
| Rounding Decimals | Adjusting a number to a specific number of decimal places based on the value of the next digit. | Used to express the cost per litre to exactly two decimal places (pennies). |
Additional Information: Unit Rates and Applications
Finding the cost per litre is an example of calculating a unit rate. A unit rate tells you how much of something per one unit of something else. Unit rates are very useful in everyday life for comparing prices or understanding efficiency.
- Comparing Prices: If you see different sizes of oil bottles, calculating the cost per litre for each can help you find the cheapest option.
- Speed: Miles per hour (miles/hour) is a common unit rate.
- Density: Mass per unit volume (e.g., grams per cubic centimeter, g/cm³) is a unit rate.
Understanding how to calculate and interpret unit rates is a fundamental skill in mathematics and practical problem-solving.
Important Questions from Inventory Control
In inventory control theory, the Economic Order Quantity is
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Bin cards are used in keeping record of -
In P - system of inventory control -
The demand rate for a particular item is 12000 units/year. The ordering cost is Rs.100 per order and the holding cost is Rs.0.80 per item per month. If no shortages are allowed and the replacement is instantaneous, then the economic order quantity is
