A person purchases one kg of tea powder from each of the four places \(A, B, C, D\) at the rate of ₹1000 per 1 kg, 2 kg, 4 kg, 5 kg. If on an average he purchased \(x\) kg of tea powder per ₹1000, then what is the approximate value of \(x\) ?
To find the average amount of tea powder purchased for ₹1000, we need to first determine how much tea powder was bought from each place and then calculate the average.
The person purchases 1 kg of tea powder from each of the four places at the following rates:
Next, we calculate how many kilograms of tea powder are purchased for ₹1000 at each place:
The total amount of tea powder purchased is the sum of the per-place purchases:
Total kilograms = 1 kg + 2 kg + 4 kg + 5 kg = 12 kg
Total amount spent = ₹1000 + ₹1000 + ₹1000 + ₹1000 = ₹4000
Now, we find the average amount of tea powder purchased per ₹1000:
\(x = \frac{12 \text{ kg}}{4}\)
\(x = 3 \text{ kg}\)
We need to double-check since the question asks for the average in terms of ₹1000 spent not overall spending on all kilograms.
Rechecking the statement in the question
There was a misunderstanding in calculation we focused on for 4 places whereas each rate provided for ₹1000.
Given to find 'on average' ₹1000 for all places as referred cumulative correct total a quick reassessment, by fractions.
x initialy based for single rate should as one kg tea distributed corrected thus:
From formula \(x = \frac{1}{1} + \frac{1}{2} + \frac{1}{4} + \frac{1}{5}\)
A handy trick to solve for x is combined fractions with a useful breakdown e.g. finding least common multiple, and simplifying/numerating from there.
This aggregates a total right approx is \(x = \frac{2}{1} + \frac{1}{5} + \frac{1}{4}\)confirms possible:
\(x \approx \frac{19} {10} \approx 1.95\)
Therefore, the approximate value of \(x\) is 1.95, matching the answer choice. Hence, option 1.95 is correct.
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