Rekha sells a DVD player to Lizaat a profit of 15% and Lizasells it Megha at a profit of 25%. If Megha pays ₹ 2875 for it, then what wasthe cost price for Rekha.

Options

A. ₹1800
B. ₹2000
C. ₹1500
D. ₹1900

Answer

To find the cost price for Rekha, we need to work backwards from the selling price Megha paid for the DVD player. Let's break down the steps:

### Step 1: Understand the Selling Price (SP) of Megha
Megha pays ₹2875 for the DVD player.

### Step 2: Calculate the Cost Price (CP) for Liza
Liza sells the DVD player to Megha at a profit of 25%. We can use the formula for selling price:
\[ \text{SP} = \text{CP} + \text{Profit} \]
Where:
- Profit = CP × (Profit % / 100)

Rearranging this, we can express CP in terms of SP:
\[ \text{CP} = \frac{\text{SP} \times 100}{100 + \text{Profit \%}} \]

Substituting the values:
\[ \text{CP of Liza} = \frac{2875 \times 100}{100 + 25} \]
\[ = \frac{2875 \times 100}{125} \]

### Step 3: Calculate the CP of Liza
Now we compute:
\[ = \frac{287500}{125} \]
\[ = 2300 \]

So, the cost price for Liza is ₹2300.

### Step 4: Calculate the Cost Price (CP) for Rekha
Now, we know that Rekha sells the DVD player to Liza at a profit of 15%. We will use the same formula:
\[ \text{CP of Rekha} = \frac{\text{SP of Liza} \times 100}{100 + \text{Profit \%}} \]

Substituting the values:
\[ \text{CP of Rekha} = \frac{2300 \times 100}{100 + 15} \]
\[ = \frac{2300 \times 100}{115} \]

### Step 5: Calculate the CP of Rekha
Now we compute:
\[ = \frac{230000}{115} \]
\[ = 2000 \]

Thus, the cost price for Rekha is ₹2000.

### Final Answer
The cost price for Rekha is ₹2000.

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