A person usually spent Rs. 48 to buy groundnuts for roasting and resale. On one occasion he could buy 1.5 kg of groundnut less for Rs 48 as the price had gone up by `25%` . What was the earlier price of groundnut per kg?

Answer

To find the earlier price of groundnut per kg, we can follow these steps:

### Step 1: Define the variables
Let the earlier price of groundnuts per kg be \( x \) Rs.

### Step 2: Calculate the new price after the increase
The price of groundnuts increased by 25%. Therefore, the new price per kg can be calculated as:
\[ \text{New Price} = x + 0.25x = 1.25x \]

### Step 3: Determine the quantity of groundnuts bought
At the earlier price \( x \), the quantity of groundnuts that could be bought for Rs. 48 is:
\[ \text{Quantity}_{\text{earlier}} = \frac{48}{x} \]

At the new price \( 1.25x \), the quantity of groundnuts that can be bought for Rs. 48 is:
\[ \text{Quantity}_{\text{new}} = \frac{48}{1.25x} \]

### Step 4: Set up the equation based on the given information
According to the problem, the person could buy 1.5 kg less groundnuts at the new price. Therefore, we can set up the equation:
\[ \frac{48}{x} - \frac{48}{1.25x} = 1.5 \]

### Step 5: Simplify the equation
To simplify, we can find a common denominator:
\[ \frac{48 \cdot 1.25 - 48}{1.25x} = 1.5 \]
\[ \frac{48(1.25 - 1)}{1.25x} = 1.5 \]
\[ \frac{48 \cdot 0.25}{1.25x} = 1.5 \]
\[ \frac{12}{1.25x} = 1.5 \]

### Step 6: Cross-multiply to solve for \( x \)
Cross-multiplying gives:
\[ 12 = 1.5 \cdot 1.25x \]
\[ 12 = 1.875x \]

### Step 7: Solve for \( x \)
Dividing both sides by 1.875:
\[ x = \frac{12}{1.875} \]
Calculating this gives:
\[ x = 6.4 \]

### Conclusion
The earlier price of groundnuts per kg was Rs. 6.4.

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