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:

• Place A: ₹1000 per 1 kg
• Place B: ₹1000 per 2 kg
• Place C: ₹1000 per 4 kg
• Place D: ₹1000 per 5 kg

Next, we calculate how many kilograms of tea powder are purchased for ₹1000 at each place:

• Place A: 1 kg for ₹1000
• Place B: 2 kg for ₹1000
• Place C: 4 kg for ₹1000
• Place D: 5 kg for ₹1000

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.