Yash sells vegetables at 40 per kg and incurs a loss of 10%. If the total loss incuired is 144, what is the weight of vegetables sold? (Rounded off)
A. 36 kg
B. 32.40 kg
C. 35 kg
D. 39.2 kg

Options

A. A
B. B
C. D
D. C

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Understand the Loss
Yash incurs a loss of 10% on the cost price (CP) of the vegetables. The total loss incurred is Rs. 144.

### Step 2: Calculate the Total Cost Price
Since the loss is 10%, this means that the selling price (SP) is 90% of the cost price. We can set up the equation for the total loss:
\[ \text{Total Loss} = \text{Cost Price} \times \frac{10}{100} \]
Given that the total loss is Rs. 144, we can express the total cost price (CP) as:
\[ 144 = \text{CP} \times \frac{10}{100} \]
To find the total cost price (CP), we rearrange the equation:
\[ \text{CP} = \frac{144 \times 100}{10} = 1440 \text{ Rs.} \]

### Step 3: Calculate the Selling Price per kg
Yash sells the vegetables at Rs. 40 per kg.

### Step 4: Calculate the Cost Price per kg
Since there is a 10% loss, the selling price is 90% of the cost price. We can express this as:
\[ \text{SP} = \text{CP} \times \frac{90}{100} \]
Substituting the selling price:
\[ 40 = \text{CP} \times \frac{90}{100} \]
Rearranging gives us:
\[ \text{CP} = \frac{40 \times 100}{90} = \frac{4000}{90} = \frac{400}{9} \text{ Rs. per kg} \]

### Step 5: Calculate the Weight of Vegetables Sold
Now that we have the total cost price (CP) and the cost price per kg, we can find the weight (x) of the vegetables sold:
\[ \text{Total CP} = \text{Weight} \times \text{CP per kg} \]
Substituting the values:
\[ 1440 = x \times \frac{400}{9} \]
To find x, we rearrange the equation:
\[ x = 1440 \times \frac{9}{400} \]
Calculating this gives:
\[ x = \frac{1440 \times 9}{400} = \frac{12960}{400} = 32.40 \text{ kg} \]

### Final Answer
The weight of the vegetables sold is **32.40 kg**.