A tape-recorder is sold for 2,760 at a gain of 15% and a C.D. player is sold for Rs 3,240 at a loss of 10%. Find :
the gain % or the loss% on the whole.

Answer

To find the overall gain or loss percentage when a tape recorder is sold at a gain of 15% and a CD player is sold at a loss of 10%, we can follow these steps:

### Step 1: Calculate the Cost Price of the Tape Recorder
Given:
- Selling Price (SP1) of the tape recorder = Rs 2760
- Gain % = 15%

Using the formula for selling price:
\[ SP = CP + \text{Gain} \]
Where Gain = \( \frac{15}{100} \times CP \)

We can rewrite the equation as:
\[ SP1 = CP1 + 0.15 \times CP1 \]
This simplifies to:
\[ SP1 = CP1 \times (1 + 0.15) \]
\[ 2760 = CP1 \times 1.15 \]

Now, solving for CP1:
\[ CP1 = \frac{2760}{1.15} \]
Calculating this gives:
\[ CP1 = 2400 \]

### Step 2: Calculate the Cost Price of the CD Player
Given:
- Selling Price (SP2) of the CD player = Rs 3240
- Loss % = 10%

Using the formula for selling price:
\[ SP = CP - \text{Loss} \]
Where Loss = \( \frac{10}{100} \times CP \)

We can rewrite the equation as:
\[ SP2 = CP2 - 0.10 \times CP2 \]
This simplifies to:
\[ SP2 = CP2 \times (1 - 0.10) \]
\[ 3240 = CP2 \times 0.90 \]

Now, solving for CP2:
\[ CP2 = \frac{3240}{0.90} \]
Calculating this gives:
\[ CP2 = 3600 \]

### Step 3: Calculate Total Cost Price and Total Selling Price
Now we can calculate the total cost price (CP) and total selling price (SP):
- Total CP = CP1 + CP2 = 2400 + 3600 = 6000
- Total SP = SP1 + SP2 = 2760 + 3240 = 6000

### Step 4: Calculate Overall Gain or Loss
To find the overall gain or loss:
\[ \text{Overall Gain or Loss} = \text{Total SP} - \text{Total CP} \]
\[ \text{Overall Gain or Loss} = 6000 - 6000 = 0 \]

### Step 5: Calculate Overall Gain or Loss Percentage
Since there is no overall gain or loss:
\[ \text{Gain or Loss Percentage} = \left( \frac{\text{Overall Gain or Loss}}{\text{Total CP}} \right) \times 100 \]
\[ \text{Gain or Loss Percentage} = \left( \frac{0}{6000} \right) \times 100 = 0\% \]

### Final Answer:
There is no gain or loss on the whole transaction, so the overall gain or loss percentage is **0%**.

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