Raju sold his old car at Rs. 1.80 lakhs at a loss of 20%. At what price had he purchased the car?

Answer

To find the cost price (CP) of Raju's car, we can use the relationship between cost price, selling price (SP), and loss percentage. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Selling Price (SP) = Rs. 1.80 lakhs
- Loss Percentage = 20%

### Step 2: Use the formula to find Cost Price (CP)
The formula to find the cost price when there is a loss is given by:
\[ CP = \frac{100}{100 - \text{Loss Percentage}} \times SP \]

### Step 3: Substitute the values into the formula
Substituting the values we have:
\[ CP = \frac{100}{100 - 20} \times 1.80 \]
\[ CP = \frac{100}{80} \times 1.80 \]

### Step 4: Simplify the fraction
Now, simplify the fraction:
\[ CP = \frac{100}{80} \times 1.80 = \frac{100 \times 1.80}{80} \]
\[ CP = \frac{180}{80} \]

### Step 5: Further simplify the fraction
Now, simplify \( \frac{180}{80} \):
- Divide both the numerator and denominator by 20:
\[ CP = \frac{180 \div 20}{80 \div 20} = \frac{9}{4} \]

### Step 6: Convert to decimal form
Now convert \( \frac{9}{4} \) to decimal:
\[ CP = 2.25 \text{ lakhs} \]

### Final Answer
Thus, Raju purchased the car for Rs. 2.25 lakhs.

---