Selling price of first article is Rs. 960 and cost price of second article is Rs. 960. If there is a profit of 20% onfirst article and loss of 20% on second article, then what will be the total loss?

Options

A. Rs. 36
B. Rs. 24
C. Rs. 20
D. Rs. 32

Answer

To solve the problem step-by-step, we will calculate the cost price (CP) of the first article, the selling price (SP) of the second article, and then determine the total loss incurred.

### Step 1: Calculate the Cost Price of the First Article
Given that the selling price (SP) of the first article is Rs. 960 and there is a profit of 20%, we can use the formula for profit:

\[ \text{SP} = \text{CP} + \text{Profit} \]

Since profit is 20% of the cost price (CP), we can express it as:

\[ \text{Profit} = 0.20 \times \text{CP} \]

Thus, the equation becomes:

\[ 960 = \text{CP} + 0.20 \times \text{CP} \]

This can be simplified to:

\[ 960 = 1.20 \times \text{CP} \]

Now, solving for CP:

\[ \text{CP} = \frac{960}{1.20} = 800 \]

### Step 2: Calculate the Selling Price of the Second Article
The cost price (CP) of the second article is given as Rs. 960, and there is a loss of 20%. The selling price (SP) in the case of a loss can be calculated as:

\[ \text{SP} = \text{CP} - \text{Loss} \]

Where loss is 20% of the cost price:

\[ \text{Loss} = 0.20 \times \text{CP} = 0.20 \times 960 = 192 \]

Thus, the selling price becomes:

\[ \text{SP} = 960 - 192 = 768 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now, we can calculate the total cost price (CP) and total selling price (SP) of both articles:

- Total CP = CP of first article + CP of second article
\[ \text{Total CP} = 800 + 960 = 1760 \]

- Total SP = SP of first article + SP of second article
\[ \text{Total SP} = 960 + 768 = 1728 \]

### Step 4: Calculate Total Loss
Finally, we can find the total loss by subtracting the total selling price from the total cost price:

\[ \text{Total Loss} = \text{Total CP} - \text{Total SP} \]
\[ \text{Total Loss} = 1760 - 1728 = 32 \]

### Conclusion
The total loss incurred is Rs. 32.

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