A man sold two articles for 1.200 each. In one. he gained 20% and on the other, he lost 20%. His total loss was-

Options

A. ₹ 400
B. ₹ 300
C. ₹ 200
D. ₹ 100

Answer

To find the total loss incurred by the man who sold two articles for 1,200 each, we can follow these steps:

### Step 1: Calculate the Cost Price of Article 1
The selling price (SP) of Article 1 is 1,200, and he gained a profit of 20%.

Using the formula for selling price with profit:
\[ SP = CP + \text{Profit} = CP + \left(\frac{20}{100} \times CP\right) = CP \left(1 + \frac{20}{100}\right) = CP \left(\frac{120}{100}\right) = CP \left(\frac{6}{5}\right) \]

Setting the selling price equal to 1,200:
\[ 1200 = CP \left(\frac{6}{5}\right) \]

Now, solving for the cost price (CP):
\[ CP = 1200 \times \frac{5}{6} = 1000 \]

### Step 2: Calculate the Cost Price of Article 2
The selling price (SP) of Article 2 is also 1,200, but he incurred a loss of 20%.

Using the formula for selling price with loss:
\[ SP = CP - \text{Loss} = CP - \left(\frac{20}{100} \times CP\right) = CP \left(1 - \frac{20}{100}\right) = CP \left(\frac{80}{100}\right) = CP \left(\frac{4}{5}\right) \]

Setting the selling price equal to 1,200:
\[ 1200 = CP \left(\frac{4}{5}\right) \]

Now, solving for the cost price (CP):
\[ CP = 1200 \times \frac{5}{4} = 1500 \]

### Step 3: Calculate Total Cost Price
Now, we can find the total cost price of both articles:
\[ \text{Total CP} = CP_{Article 1} + CP_{Article 2} = 1000 + 1500 = 2500 \]

### Step 4: Calculate Total Selling Price
The total selling price of both articles is:
\[ \text{Total SP} = SP_{Article 1} + SP_{Article 2} = 1200 + 1200 = 2400 \]

### Step 5: Calculate Total Loss
Finally, we can calculate the total loss:
\[ \text{Total Loss} = \text{Total CP} - \text{Total SP} = 2500 - 2400 = 100 \]

Thus, the total loss incurred by the man is **100 rupees**.

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