What was the cost price of the suitcase purchased by Richard ?
(i) Richard got `20%` concession on the labelled price.
(ii) Richard sold the suitcase for Rs. 2000 with `25%` profit on the labelled price.

Answer

To find the cost price of the suitcase purchased by Richard, we can follow these steps:

### Step 1: Understand the Selling Price and Profit
Richard sold the suitcase for Rs. 2000 with a 25% profit on the labelled price (LP). This means that the selling price (SP) is 125% of the labelled price (LP).

### Step 2: Calculate the Labelled Price
Let the labelled price be \( LP \). Since Richard sold the suitcase for Rs. 2000, we can set up the equation:
\[ SP = LP \times \frac{125}{100} \]
Substituting the selling price:
\[ 2000 = LP \times \frac{125}{100} \]
To find \( LP \):
\[ LP = 2000 \times \frac{100}{125} = 2000 \times 0.8 = 1600 \]

### Step 3: Calculate the Cost Price
Richard received a 20% concession on the labelled price. Therefore, the cost price (CP) can be calculated as follows:
\[ CP = LP - (20\% \text{ of } LP) \]
Calculating 20% of the labelled price:
\[ 20\% \text{ of } 1600 = 0.2 \times 1600 = 320 \]
Now, substituting this back to find the cost price:
\[ CP = 1600 - 320 = 1280 \]

### Conclusion
The cost price of the suitcase purchased by Richard is Rs. 1280.

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