The average cost of a pencil is ₹8 and the average cost of an eraser is ₹4. The cost of 8 erasers, 4 pencils and 12 sharpeners are ₹148. The average cost of a sharpener is ₹ ______.
Calculating the Average Cost of a Sharpener
This problem involves calculating the average cost of a sharpener given the costs of pencils and erasers, and the total cost of a mixed purchase.
Understanding the Given Information
- Average cost of one pencil: ₹8
- Average cost of one eraser: ₹4
- Total cost of 8 erasers, 4 pencils, and 12 sharpeners: ₹148
- We need to find the average cost of one sharpener.
Step-by-Step Calculation
Follow these steps to find the average cost of a sharpener:
1. Calculate the Total Cost of Erasers
We have 8 erasers, and each costs ₹4.
Total cost of erasers = Number of erasers $\times$ Cost per eraser
Total cost of erasers = $8 \times \text{₹}4 = \text{₹}32
2. Calculate the Total Cost of Pencils
We have 4 pencils, and each costs ₹8.
Total cost of pencils = Number of pencils $\times$ Cost per pencil
Total cost of pencils = $4 \times \text{₹}8 = \text{₹}32
3. Calculate the Combined Cost of Erasers and Pencils
Add the costs calculated in the previous steps.
Combined cost = Total cost of erasers + Total cost of pencils
Combined cost = $\text{₹}32 + \text{₹}32 = \text{₹}64
4. Calculate the Total Cost of Sharpeners
The total cost includes erasers, pencils, and sharpeners. Subtract the combined cost of erasers and pencils from the total cost.
Total cost of sharpeners = Total purchase cost - Combined cost of erasers and pencils
Total cost of sharpeners = $\text{₹}148 - \text{₹}64 = \text{₹}84
5. Calculate the Average Cost of a Sharpener
We have 12 sharpeners whose total cost is ₹84. To find the average cost, divide the total cost by the number of sharpeners.
Average cost of a sharpener = Total cost of sharpeners / Number of sharpeners
Average cost of a sharpener = $\text{₹}84 / 12
Average cost of a sharpener = $\text{₹}7
Conclusion
The average cost of a sharpener is ₹7.
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