Calculating Total Cost of Groceries
This problem requires us to find the total cost of specific quantities of sugar, tea, and rice. We are given the cost for certain amounts of each item and need to calculate the cost for different amounts. The first step is always to find the price per unit (in this case, per kilogram) for each item.
Determining Unit Costs for Each Item
Let's break down the cost per kilogram for sugar, tea, and rice.
1. Unit Cost of Sugar
We know that 15 kg of sugar costs Rs. 255.
To find the cost of 1 kg of sugar, we perform the following calculation:
Cost per kg of Sugar = \(\frac{\text{Total Cost of Sugar}}{\text{Quantity of Sugar}}\)
Cost per kg of Sugar = \(\frac{Rs. 255}{15 \text{ kg}}\)
Cost per kg of Sugar = Rs. 17 per kg
2. Unit Cost of Tea
We are given that 17 kg of tea costs Rs. 1,615.
To find the cost of 1 kg of tea:
Cost per kg of Tea = \(\frac{\text{Total Cost of Tea}}{\text{Quantity of Tea}}\)
Cost per kg of Tea = \(\frac{Rs. 1,615}{17 \text{ kg}}\)
Cost per kg of Tea = Rs. 95 per kg
3. Unit Cost of Rice
We are given that 22 kg of rice costs Rs. 572.
To find the cost of 1 kg of rice:
Cost per kg of Rice = \(\frac{\text{Total Cost of Rice}}{\text{Quantity of Rice}}\)
Cost per kg of Rice = \(\frac{Rs. 572}{22 \text{ kg}}\)
Cost per kg of Rice = Rs. 26 per kg
Calculating the Cost for Required Quantities
Now that we have the cost per kilogram for each item, we can calculate the cost for the specified quantities.
1. Cost of 18 kg of Sugar
Using the unit cost of sugar (Rs. 17 per kg):
Cost of 18 kg Sugar = 18 kg \(\times\) Rs. 17 per kg
Cost of 18 kg Sugar = Rs. 306
2. Cost of 21 kg of Tea
Using the unit cost of tea (Rs. 95 per kg):
Cost of 21 kg Tea = 21 kg \(\times\) Rs. 95 per kg
Cost of 21 kg Tea = Rs. 1,995
3. Cost of 27 kg of Rice
Using the unit cost of rice (Rs. 26 per kg):
Cost of 27 kg Rice = 27 kg \(\times\) Rs. 26 per kg
Cost of 27 kg Rice = Rs. 702
Summing Up the Total Cost
To find the total cost, we add the costs calculated for each item.
Total Cost = Cost of 18 kg Sugar + Cost of 21 kg Tea + Cost of 27 kg Rice
Total Cost = Rs. 306 + Rs. 1,995 + Rs. 702
Total Cost = Rs. 3,003
Summary of Calculations
| Item | Given Quantity & Cost | Calculated Cost per kg | Required Quantity | Calculated Cost for Required Quantity |
| Sugar | 15 kg = Rs. 255 | Rs. 17 | 18 kg | Rs. 306 |
| Tea | 17 kg = Rs. 1,615 | Rs. 95 | 21 kg | Rs. 1,995 |
| Rice | 22 kg = Rs. 572 | Rs. 26 | 27 kg | Rs. 702 |
| Total Cost | Rs. 3,003 | |||
Therefore, the total cost for 18 kg of sugar, 21 kg of tea, and 27 kg of rice is Rs. 3,003.
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