A trader sells two articles for Rs. 1875 each. If he gains 25% on one and loses 25% on other, then what is the value (in Rs.) of the loss?

Options

A. 150
B. 250
C. 400
D. 500

Answer

To solve the problem, we need to determine the cost price of each article based on the selling price and the profit/loss percentages.

**Step 1: Calculate the cost price of the first article.**

Let the cost price of the first article be \( CP_1 \).

Given that the selling price (SP) of the first article is Rs. 1875 and the gain is 25%, we can use the formula for selling price:

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

Since Gain = 25% of \( CP_1 \), we can express it as:

\[ SP = CP_1 + 0.25 \times CP_1 = 1.25 \times CP_1 \]

Substituting the selling price:

\[ 1875 = 1.25 \times CP_1 \]

Now, we can solve for \( CP_1 \):

\[ CP_1 = \frac{1875}{1.25} = 1500 \]

**Step 2: Calculate the cost price of the second article.**

Let the cost price of the second article be \( CP_2 \).

Given that the selling price (SP) of the second article is also Rs. 1875 and the loss is 25%, we can use the formula for selling price:

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

Since Loss = 25% of \( CP_2 \), we can express it as:

\[ SP = CP_2 - 0.25 \times CP_2 = 0.75 \times CP_2 \]

Substituting the selling price:

\[ 1875 = 0.75 \times CP_2 \]

Now, we can solve for \( CP_2 \):

\[ CP_2 = \frac{1875}{0.75} = 2500 \]

**Step 3: Calculate the total cost price and the total selling price.**

Total Cost Price (TCP) = \( CP_1 + CP_2 = 1500 + 2500 = 4000 \)

Total Selling Price (TSP) = Selling price of both articles = \( 1875 + 1875 = 3750 \)

**Step 4: Calculate the overall loss.**

Overall Loss = Total Cost Price - Total Selling Price

\[ \text{Overall Loss} = TCP - TSP = 4000 - 3750 = 250 \]

Thus, the value of the loss is Rs. 250.

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