6. A customer paid Ksh 5880 for a suit after she was allowed a discount of $$ 2 \% $$ on the selling price. If the discount had not been allowed, the shopkeeper would have made a profit of $$ 20 \% $$ on the sale of the suit. Calculate the price at which th shopkeeper bought the suit. ( 3 marks)

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To find the price at which the shopkeeper bought the suit, we can follow these steps:

1. **Let the selling price (SP) of the suit be $$ x $$.**
2. **The customer received a discount of $$ 2\% $$ on the selling price.** Therefore, the price paid by the customer can be expressed as:
   $$
   \text{Price paid} = x - 0.02x = 0.98x
   $$
   We know that the price paid is Ksh 5880, so we can set up the equation:
   $$
   0.98x = 5880
   $$

3. **Solve for $$ x $$:**
   $$
   x = \frac{5880}{0.98} = 6000
   $$
   So, the selling price (SP) of the suit is Ksh 6000.

4. **The shopkeeper would have made a profit of $$ 20\% $$ on the sale of the suit if the discount had not been allowed.** This means that the cost price (CP) can be calculated using the formula for profit:
   $$
   \text{Selling Price} = \text{Cost Price} + \text{Profit}
   $$
   Since the profit is $$ 20\% $$ of the cost price, we can express this as:
   $$
   SP = CP + 0.20 \times CP = 1.20 \times CP
   $$
   Substituting the selling price:
   $$
   6000 = 1.20 \times CP
   $$

5. **Now, solve for $$ CP $$:**
   $$
   CP = \frac{6000}{1.20} = 5000
   $$

Thus, the price at which the shopkeeper bought the suit is **Ksh 5000**.
The shopkeeper bought the suit for Ksh 5000.

6. A customer paid Ksh 5880 for a suit after she was allowed a discount of \( 2 \% \) on the selling price. If the discount had not been allowed, the shopkeeper would have made a profit of \( 20 \% \) on the sale of the suit. Calculate the price at which th shopkeeper bought the suit. ( 3 marks)

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