Suhana sells a sofa set for Rs. 9600 making a profit of 20%. What is the C.P. of the sofa set?

Answer

To find the cost price (C.P.) of the sofa set that Suhana sold for Rs. 9600 with a profit of 20%, we can follow these steps:

### Step 1: Understand the relationship between Selling Price, Cost Price, and Profit
The Selling Price (S.P.) is given by the formula:
\[ \text{S.P.} = \text{C.P.} + \text{Profit} \]
We can express Profit in terms of Cost Price:
\[ \text{Profit} = \text{Profit Percentage} \times \text{C.P.} \]
In this case, the Profit Percentage is 20%, which can be expressed as a fraction:
\[ \text{Profit} = \frac{20}{100} \times \text{C.P.} = \frac{1}{5} \times \text{C.P.} \]

### Step 2: Substitute the values into the equation
Now we can substitute the values we know into the equation:
\[ 9600 = \text{C.P.} + \frac{1}{5} \times \text{C.P.} \]

### Step 3: Combine like terms
To combine the terms on the right side, we can express \(\text{C.P.}\) as a fraction:
\[ 9600 = \text{C.P.} + \frac{1}{5} \text{C.P.} = \frac{5}{5} \text{C.P.} + \frac{1}{5} \text{C.P.} = \frac{6}{5} \text{C.P.} \]

### Step 4: Solve for C.P.
Now we can solve for C.P. by multiplying both sides of the equation by 5:
\[ 9600 \times 5 = 6 \text{C.P.} \]
This simplifies to:
\[ 48000 = 6 \text{C.P.} \]
Now, divide both sides by 6:
\[ \text{C.P.} = \frac{48000}{6} = 8000 \]

### Conclusion
Therefore, the cost price of the sofa set is Rs. 8000.

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