A reduction of 10 % in the price of tea would enable and purchase to obtain 3kg . More for 2700 Rs. Find the reduced rate ( new rate ) of tea .

Answer

To solve the problem step by step, we will follow the reasoning presented in the video transcript.

### Step 1: Define the original price of tea
Let the original price of tea be \( x \) Rs per kg.

### Step 2: Calculate the reduced price after a 10% reduction
A reduction of 10% in the price means the new price will be:
\[ \text{New Price} = x - 0.1x = 0.9x = \frac{9}{10}x \text{ Rs per kg} \]

### Step 3: Determine how much tea can be bought at the new price
According to the problem, with the reduced price, a person can buy 3 kg more tea for 2700 Rs.
The amount of tea that can be bought at the new price is:
\[ \text{Amount of tea at new price} = \frac{2700}{\frac{9}{10}x} = \frac{2700 \times 10}{9x} = \frac{27000}{9x} = \frac{3000}{x} \text{ kg} \]

### Step 4: Determine how much tea could be bought at the original price
At the original price, the amount of tea that could be bought for 2700 Rs is:
\[ \text{Amount of tea at original price} = \frac{2700}{x} \text{ kg} \]

### Step 5: Set up the equation based on the problem statement
According to the problem, the difference in the amount of tea bought at the new price and the original price is 3 kg:
\[ \frac{3000}{x} - \frac{2700}{x} = 3 \]

### Step 6: Simplify the equation
Combine the fractions:
\[ \frac{3000 - 2700}{x} = 3 \]
\[ \frac{300}{x} = 3 \]

### Step 7: Solve for \( x \)
Cross-multiply to solve for \( x \):
\[ 300 = 3x \]
\[ x = \frac{300}{3} = 100 \text{ Rs per kg} \]

### Step 8: Calculate the reduced price
Now, we can find the reduced price:
\[ \text{Reduced Price} = \frac{9}{10} \times 100 = 90 \text{ Rs per kg} \]

### Final Answer
The reduced rate (new rate) of tea is **90 Rs per kg**.

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