X kilogram tea costing Rs. 180/kg is mixed with X kilogram tea costing Rs. 240/kg. What is the cost (per kg) of the mixture?a)Rs. 180/kgb)Rs. 200/kgc)Rs. 210/kgd)Rs. 240/kgCorrect answer is option 'C'. Can you explain this answer?

Question

Answer

Understanding the Problem
In this problem, we have two types of tea being mixed:
- X kg of tea costing Rs. 180/kg
- X kg of tea costing Rs. 240/kg
Our goal is to find the cost per kg of the resulting mixture.
Calculating Total Cost
1. Cost of the First Tea
- Cost for X kg of tea at Rs. 180/kg:
Total Cost = X * 180 = 180X
2. Cost of the Second Tea
- Cost for X kg of tea at Rs. 240/kg:
Total Cost = X * 240 = 240X
3. Total Cost of the Mixture
- Total Cost = Cost of First Tea + Cost of Second Tea
Total Cost = 180X + 240X = 420X
Calculating Total Weight
- Total Weight of the Mixture = X kg + X kg = 2X kg
Cost Per Kg of the Mixture
- Cost Per Kg = Total Cost / Total Weight
Cost Per Kg = (420X) / (2X) = 210
Thus, the cost per kg of the mixture is Rs. 210.
Conclusion
The correct answer is option 'C' - Rs. 210/kg. This solution demonstrates how to combine different costs and weights to find an average cost, applicable in various scenarios beyond just tea mixtures.

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