Two articles are sold for Rs. 4,752 each. One one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percent, correct to one decimal place ?

Options

A. 7.3 % gain
B. 7.3 % loss
C. 6.8% loss
D. 6.8% gain

Answer

To find the overall gain or loss percent when two articles are sold at different profit and loss percentages, we can follow these steps:

### Step 1: Calculate the Cost Price of Each Article

Let the cost price of the first article be \( CP_1 \) and the cost price of the second article be \( CP_2 \).

For the first article, the selling price (SP) is Rs. 4,752, and the gain is 32%.

Using the formula for selling price:
\[ SP = CP + \text{Gain} \]
We can express the gain in terms of cost price:
\[ SP = CP_1 + 0.32 \times CP_1 = 1.32 \times CP_1 \]
Thus,
\[ CP_1 = \frac{SP}{1.32} = \frac{4752}{1.32} \]

Calculating \( CP_1 \):
\[ CP_1 = \frac{4752}{1.32} \approx 3,600 \]

For the second article, the selling price is also Rs. 4,752, and the loss is 28%.

Using the formula for selling price with loss:
\[ SP = CP - \text{Loss} \]
We can express the loss in terms of cost price:
\[ SP = CP_2 - 0.28 \times CP_2 = 0.72 \times CP_2 \]
Thus,
\[ CP_2 = \frac{SP}{0.72} = \frac{4752}{0.72} \]

Calculating \( CP_2 \):
\[ CP_2 = \frac{4752}{0.72} \approx 6,600 \]

### Step 2: Calculate the Total Cost Price and Total Selling Price

Now, we can find the total cost price (TCP) and total selling price (TSP):

\[ TCP = CP_1 + CP_2 = 3600 + 6600 = 10200 \]
\[ TSP = SP_1 + SP_2 = 4752 + 4752 = 9504 \]

### Step 3: Calculate Overall Gain or Loss

Now, we can find the overall gain or loss:
\[ \text{Overall Gain/Loss} = TSP - TCP = 9504 - 10200 = -696 \]

Since the result is negative, it indicates a loss.

### Step 4: Calculate the Overall Loss Percent

To find the loss percent, we use the formula:
\[ \text{Loss Percent} = \left( \frac{\text{Loss}}{\text{Total Cost Price}} \right) \times 100 \]
Substituting the values:
\[ \text{Loss Percent} = \left( \frac{696}{10200} \right) \times 100 \approx 6.82 \]

### Final Answer

Rounding to one decimal place, the overall loss percent is:
\[ \text{Overall Loss Percent} \approx 6.8\% \]

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