Question

Details of prices of two items P and Q are presented in the above table. The ratio of cost of item P to cost of item Q is 3:4. Discount is calculated as the difference between the marked price and the selling price. The profit percentage is calculated as the ratio of the difference between selling price and cost, to the cost. 
The formula for Profit Percentage is: 
\[ \text{Profit \%} = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100 \] The discount on item Q, as a percentage of its marked price, is: 

• A. 25
• B. 12.5
• C. 10
• D. 5

Hint:

The profit percentage helps in calculating the selling price. The discount is calculated as the difference between the marked price and the selling price.

Answer 1

The Correct Option is C

We are given the following data: 
- Cost of item P = ₹5400 
- Marked price of item P = ₹5860 
- Profit on item Q = 25% 
- Marked price of item Q = ₹10,000 
Step 1: Calculating the selling price of item P 
The profit percentage on item P can be calculated using the formula: \[ \text{Profit \%} = \frac{\text{Selling Price} - \text{Cost}}{\text{Cost}} \times 100 \] Substituting the known values for item P: \[ \text{Profit \%} = \frac{5860 - 5400}{5400} \times 100 = \frac{460}{5400} \times 100 \approx 8.52% \] Thus, the profit percentage on item P is approximately 8.52%. Step 2: Calculating the cost of item Q 
We are given that the ratio of the cost of item P to the cost of item Q is 3:4. Thus: \[ \frac{\text{Cost of P}}{\text{Cost of Q}} = \frac{3}{4} \] Using the given cost of item P (₹5400), we can calculate the cost of item Q: \[ \text{Cost of Q} = \frac{4}{3} \times 5400 = 7200 \] Step 3: Calculating the selling price of item Q 
We know the profit percentage on item Q is 25%. Using the formula for profit percentage: \[ 25 = \frac{\text{Selling Price of Q} - \text{Cost of Q}}{\text{Cost of Q}} \times 100 \] Substituting the values for the cost of item Q: \[ 25 = \frac{\text{Selling Price of Q} - 7200}{7200} \times 100 \] \[ \text{Selling Price of Q} = 7200 + \frac{25 \times 7200}{100} = 7200 + 1800 = 9000 \] Step 4: Calculating the discount on item Q 
The discount is the difference between the marked price and the selling price. For item Q: \[ \text{Discount} = 10000 - 9000 = 1000 \] The discount percentage is calculated as: \[ \text{Discount Percentage} = \frac{1000}{10000} \times 100 = 10% \] Thus, the discount on item Q as a percentage of its marked price is 10%, and the correct answer is (C).