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 total C.P. of both.

Answer

To find the total cost price (C.P.) of both the tape recorder and the CD player, we will follow these steps:

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

We know that:
\[ \text{S.P.} = \text{C.P.} + \text{Gain} \]
Where Gain can be expressed as:
\[ \text{Gain} = \text{C.P.} \times \frac{\text{Gain \%}}{100} = \text{C.P.} \times 0.15 \]

Thus, we can rewrite the equation as:
\[ \text{S.P.} = \text{C.P.} + \text{C.P.} \times 0.15 \]
\[ \text{S.P.} = \text{C.P.} (1 + 0.15) = \text{C.P.} \times 1.15 \]

Now, substituting the given S.P.:
\[ 2760 = \text{C.P.} \times 1.15 \]

To find C.P.:
\[ \text{C.P.} = \frac{2760}{1.15} = 2400 \]

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

We know that:
\[ \text{S.P.} = \text{C.P.} - \text{Loss} \]
Where Loss can be expressed as:
\[ \text{Loss} = \text{C.P.} \times \frac{\text{Loss \%}}{100} = \text{C.P.} \times 0.10 \]

Thus, we can rewrite the equation as:
\[ \text{S.P.} = \text{C.P.} - \text{C.P.} \times 0.10 \]
\[ \text{S.P.} = \text{C.P.} (1 - 0.10) = \text{C.P.} \times 0.90 \]

Now, substituting the given S.P.:
\[ 3240 = \text{C.P.} \times 0.90 \]

To find C.P.:
\[ \text{C.P.} = \frac{3240}{0.90} = 3600 \]

### Step 3: Calculate the Total Cost Price of Both Items
Now, we can find the total C.P. of both the tape recorder and the CD player:
\[ \text{Total C.P.} = \text{C.P. of Tape Recorder} + \text{C.P. of CD Player} \]
\[ \text{Total C.P.} = 2400 + 3600 = 6000 \]

### Final Answer
The total cost price of both the tape recorder and the CD player is Rs 6000.

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