How should we mix two rice packets to get one 1kg packet priced at Rs.8 when the prices of 1 kg packets of the two types are Rs.7.1 and Rs.9.2.
Question
How should we mix two rice packets to get one 1kg packet priced at Rs.8 when the prices of 1 kg packets of the two types are Rs.7.1 and Rs.9.2.
Solution
To solve this problem, we can use the concept of weighted averages.
Let's denote the amount of rice from the first packet as x kg and from the second packet as (1-x) kg (since the total amount of rice is 1 kg).
The weighted average price of the mixed rice packet can be calculated as follows:
7.1x + 9.2(1-x) = 8
Solving this equation for x gives us the proportion of rice from the first packet that should be mixed with the rice from the second packet to get a 1 kg packet priced at Rs.8.
7.1x + 9.2 - 9.2x = 8
2.1*x = 9.2 - 8
2.1*x = 1.2
x = 1.2 / 2.1
x = 0.57 (approximately)
So, to get a 1 kg packet priced at Rs.8, we should mix approximately 0.57 kg of rice from the first packet (priced at Rs.7.1 per kg) with 0.43 kg of rice from the second packet (priced at Rs.9.2 per kg).
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