A man sold two radias at₹4800 each. On one he gains 20% and on the other he loses 20%.Find the gain or loss per cent in the whole transaction.

Answer

To solve the problem, we need to find the total cost price (CP) and total selling price (SP) of the two radias and then determine the overall gain or loss percentage. Let's break it down step by step.

### Step 1: Calculate the Cost Price of the First Radia
The selling price (SP) of the first radia is ₹4800, and he gains 20% on it.

Let the cost price (CP) of the first radia be \( x \).

Using the formula for selling price with gain:
\[ SP = CP + \text{Gain} \]
Where Gain = 20% of CP = \( \frac{20}{100} \times x = 0.2x \)

So,
\[ 4800 = x + 0.2x \]
\[ 4800 = 1.2x \]

Now, solve for \( x \):
\[ x = \frac{4800}{1.2} = 4000 \]

### Step 2: Calculate the Cost Price of the Second Radia
The selling price (SP) of the second radia is also ₹4800, but he incurs a loss of 20%.

Let the cost price (CP) of the second radia be \( y \).

Using the formula for selling price with loss:
\[ SP = CP - \text{Loss} \]
Where Loss = 20% of CP = \( \frac{20}{100} \times y = 0.2y \)

So,
\[ 4800 = y - 0.2y \]
\[ 4800 = 0.8y \]

Now, solve for \( y \):
\[ y = \frac{4800}{0.8} = 6000 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now we can find the total cost price (CP) and total selling price (SP) for both radias.

Total CP = Cost Price of First Radia + Cost Price of Second Radia
\[ \text{Total CP} = 4000 + 6000 = 10000 \]

Total SP = Selling Price of First Radia + Selling Price of Second Radia
\[ \text{Total SP} = 4800 + 4800 = 9600 \]

### Step 4: Calculate Loss
Now, we calculate the loss incurred in the whole transaction:
\[ \text{Loss} = \text{Total CP} - \text{Total SP} = 10000 - 9600 = 400 \]

### Step 5: Calculate Loss Percentage
Finally, we can find the loss percentage using the formula:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{Total CP}} \right) \times 100 \]
\[ \text{Loss Percentage} = \left( \frac{400}{10000} \right) \times 100 = 4\% \]

### Final Answer
The overall loss percentage in the whole transaction is **4%**.

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