Nikunj sold a machine to Sonia at a profit of 30%. Sonia sold this machine to Anu at a loss of 20%. If Nikunj paid Rs 5000 forth is machine,then find the cost price of machine for Anu.

Answer

To find the cost price of the machine for Anu, we will follow these steps:

### Step 1: Calculate the Selling Price of the Machine for Sonia
Nikunj sold the machine to Sonia at a profit of 30%.
- Cost Price (CP) for Nikunj = Rs. 5000
- Profit Percentage = 30%

To find the Selling Price (SP) for Sonia:
\[ SP = CP + (Profit \, \text{Percentage} \times CP) \]
\[ SP = 5000 + (0.30 \times 5000) \]
\[ SP = 5000 + 1500 = 6500 \]

### Step 2: Calculate the Cost Price of the Machine for Sonia
From the calculation above, we find that the Selling Price for Sonia is Rs. 6500. Therefore, the Cost Price for Sonia is:
\[ CP_{Sonia} = SP_{Nikunj} = 6500 \]

### Step 3: Calculate the Selling Price of the Machine for Anu
Sonia sold the machine to Anu at a loss of 20%.
- Cost Price (CP) for Sonia = Rs. 6500
- Loss Percentage = 20%

To find the Selling Price (SP) for Anu:
\[ SP = CP - (Loss \, \text{Percentage} \times CP) \]
\[ SP = 6500 - (0.20 \times 6500) \]
\[ SP = 6500 - 1300 = 5200 \]

### Step 4: Conclusion
The Selling Price for Anu is Rs. 5200, which is also the cost price of the machine for Anu.

Thus, the cost price of the machine for Anu is:
\[ \text{Cost Price for Anu} = Rs. 5200 \]

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