A man purchased sugar worth of Rs. 400 he sold (3 / 4)th at a loss of 10% and the remainder at a gain of 10%. on the whole, he gets

Options

A. A loss of `5%`
B. A gain of `(5)1/2%`
C. A loss of `(5)1/(19)%`
D. A loss of `(5)5/(19)%`

Answer

To solve the problem step by step, we will follow the calculations as described in the video transcript.

### Step 1: Determine the Cost Price of Sugar
The total cost price (CP) of the sugar is given as Rs. 400.

### Step 2: Calculate the Cost Price of (3/4)th of Sugar
To find the cost price of (3/4)th of the sugar:
\[ \text{Cost Price of } \frac{3}{4} \text{ sugar} = \frac{3}{4} \times 400 = 300 \text{ Rs.} \]

### Step 3: Calculate the Selling Price of (3/4)th of Sugar at a Loss of 10%
A loss of 10% means he sells it for 90% of the cost price. Therefore,
\[ \text{Selling Price (SP) of } \frac{3}{4} \text{ sugar} = 90\% \text{ of } 300 = \frac{90}{100} \times 300 = 270 \text{ Rs.} \]

### Step 4: Calculate the Cost Price of the Remaining (1/4)th of Sugar
The remaining sugar is (1/4)th of the total:
\[ \text{Cost Price of } \frac{1}{4} \text{ sugar} = \frac{1}{4} \times 400 = 100 \text{ Rs.} \]

### Step 5: Calculate the Selling Price of (1/4)th of Sugar at a Gain of 10%
A gain of 10% means he sells it for 110% of the cost price. Therefore,
\[ \text{Selling Price (SP) of } \frac{1}{4} \text{ sugar} = 110\% \text{ of } 100 = \frac{110}{100} \times 100 = 110 \text{ Rs.} \]

### Step 6: Calculate the Total Selling Price
Now, we add the selling prices of both portions of sugar:
\[ \text{Total Selling Price} = \text{SP of } \frac{3}{4} \text{ sugar} + \text{SP of } \frac{1}{4} \text{ sugar} = 270 + 110 = 380 \text{ Rs.} \]

### Step 7: Calculate the Loss
To find the loss, we subtract the total selling price from the total cost price:
\[ \text{Loss} = \text{Cost Price} - \text{Total Selling Price} = 400 - 380 = 20 \text{ Rs.} \]

### Step 8: Calculate the Percentage Loss
Finally, we calculate the percentage loss:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{Cost Price}} \right) \times 100 = \left( \frac{20}{400} \right) \times 100 = 5\% \]

### Final Answer
The man incurs a loss of **5%** on the whole transaction.

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