Mrs. Annapurna per day sells exactly four quintal sugar at ₹ 2000 per quintal getting the profit of ₹ `25%`. Since she mixes two varities of sugar, one costs ₹ 14 per kg and another costs ₹ 22 per kg. One day due to huge demand in market she had only 3 quintal of the required mixture so ahe purchased the sugar costs ₹ 17 per kg at ₹ 18 per kg from the wholeseller on that day and then she mixed 300 kg mixture with 100 kg sugar costing ₹ 18 per kg to fulfill the demand of the market selling at the same price. How much percent less does she gain that she would have gained, if she had sufficient quantity of used mixture of sugar?

Options

A. `12.5%`
B. `18.18%`
C. `62.5%`
D. can't be determined

Answer

To solve the problem step by step, we will first calculate the profit Mrs. Annapurna would have made if she had sufficient quantity of the mixture of sugar, and then we will calculate the profit she actually made with the sugar she purchased. Finally, we will find out how much percent less profit she made compared to what she would have made.

### Step 1: Calculate the Selling Price and Cost Price of Sugar
Mrs. Annapurna sells sugar at ₹2000 per quintal. Since 1 quintal = 100 kg, the selling price per kg is:
\[ \text{Selling Price per kg} = \frac{2000}{100} = ₹20 \]

### Step 2: Calculate the Cost Price of the Mixture
The profit is 25%, which means the cost price (CP) can be calculated as follows:
\[ \text{Selling Price} = \text{Cost Price} + \text{Profit} \]
Let the cost price be \( CP \).
\[ 20 = CP + 0.25 \times CP \]
\[ 20 = 1.25 \times CP \]
\[ CP = \frac{20}{1.25} = ₹16 \]

### Step 3: Calculate the Total Cost Price for 4 Quintals
If she sells 4 quintals (400 kg), the total cost price would be:
\[ \text{Total Cost Price} = 400 \times 16 = ₹6400 \]

### Step 4: Calculate the Total Selling Price for 4 Quintals
The total selling price for 4 quintals is:
\[ \text{Total Selling Price} = 400 \times 20 = ₹8000 \]

### Step 5: Calculate the Profit if Sufficient Quantity was Available
The profit if she had sufficient quantity of the mixture would be:
\[ \text{Profit} = \text{Total Selling Price} - \text{Total Cost Price} = 8000 - 6400 = ₹1600 \]

### Step 6: Calculate the Actual Selling Price with the New Sugar
On that day, she mixed 300 kg of sugar at ₹17 per kg with 100 kg of sugar at ₹18 per kg. The total cost for this mixture is:
\[ \text{Cost of 300 kg} = 300 \times 17 = ₹5100 \]
\[ \text{Cost of 100 kg} = 100 \times 18 = ₹1800 \]
\[ \text{Total Cost Price of Mixture} = 5100 + 1800 = ₹6900 \]

### Step 7: Calculate the Total Selling Price of the Mixture
The total selling price for the 400 kg mixture (still selling at ₹20 per kg) is:
\[ \text{Total Selling Price} = 400 \times 20 = ₹8000 \]

### Step 8: Calculate the Actual Profit
The actual profit made with the mixture is:
\[ \text{Actual Profit} = \text{Total Selling Price} - \text{Total Cost Price of Mixture} = 8000 - 6900 = ₹1100 \]

### Step 9: Calculate the Percent Less Gain
To find out how much percent less she gained compared to the profit she would have made:
\[ \text{Difference in Profit} = 1600 - 1100 = ₹500 \]
\[ \text{Percent Less Gain} = \left( \frac{500}{1600} \right) \times 100 = 31.25\% \]

### Final Answer
Mrs. Annapurna gains **31.25% less** than she would have gained if she had sufficient quantity of the mixture of sugar.

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