With a 5% discount on the cost of sugar, a buyer could purchase 2 kg more sugar for Rs. 608. Selling price of sugar is :

Options

A. Rs. 15.50
B. Rs 15
C. RS. 16.50
D. Rs. 16

Answer

To solve the problem step by step, let's break it down:

### Step 1: Understand the given information
The buyer can purchase 2 kg more sugar for Rs. 608 due to a 5% discount. We need to find the selling price of sugar.

### Step 2: Define variables
Let the original price of sugar per kg be \( P \).

### Step 3: Calculate the selling price after the discount
Since there is a 5% discount, the selling price after the discount can be calculated as:
\[ \text{Selling Price} = P - 0.05P = 0.95P \]

### Step 4: Determine the quantity of sugar purchased before and after the discount
1. **Before the discount**: The quantity of sugar that could be bought with Rs. 608 at the original price \( P \) is:
\[ \text{Quantity before discount} = \frac{608}{P} \]

2. **After the discount**: The quantity of sugar that could be bought with Rs. 608 at the discounted price \( 0.95P \) is:
\[ \text{Quantity after discount} = \frac{608}{0.95P} \]

### Step 5: Set up the equation based on the information given
According to the problem, the buyer can purchase 2 kg more sugar after the discount:
\[ \frac{608}{0.95P} = \frac{608}{P} + 2 \]

### Step 6: Simplify the equation
Multiply through by \( 0.95P \) to eliminate the denominators:
\[ 608 = 0.95 \cdot 608 + 2 \cdot 0.95P \]
\[ 608 - 0.95 \cdot 608 = 1.9P \]
\[ (1 - 0.95) \cdot 608 = 1.9P \]
\[ 0.05 \cdot 608 = 1.9P \]
\[ 30.4 = 1.9P \]

### Step 7: Solve for \( P \)
\[ P = \frac{30.4}{1.9} \approx 16 \]

### Step 8: Calculate the selling price
Now, we can find the selling price:
\[ \text{Selling Price} = 0.95P = 0.95 \cdot 16 = 15.2 \]

### Final Answer
The selling price of sugar is Rs. 15.2 per kg.

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