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

To find the discount on item Q as a percentage of its marked price, we need to first determine the selling price of item Q using the given profit percentage formula. Then, we calculate the discount.

1. Let the cost price of item Q be C_Q.
2. We know the profit percentage is 25%, so: \[\text{Profit \%} = \frac{\text{Selling Price} - C_Q}{C_Q} \times 100 = 25\]
   Simplifying, we get: \[\text{Selling Price} = C_Q \times \left(1 + \frac{25}{100}\right) = 1.25 \times C_Q\]
3. Since the ratio of the cost of item P to item Q is 3:4, and the cost of item P is 5400, we can set up the equation: \[\frac{5400}{C_Q} = \frac{3}{4}\]
   Solving this gives: C_Q = \frac{5400 \times 4}{3} = 7200
4. The selling price of item Q is: \[\text{Selling Price} = 1.25 \times 7200 = 9000\]
5. The marked price of item Q is 10,000. Thus, the discount is: \[ \text{Discount} = \text{Marked Price} - \text{Selling Price} = 10000 - 9000 = 1000\]
6. The discount percentage is calculated as: \[\text{Discount \%} = \frac{1000}{10000} \times 100 = 10\%\]

Hence, the discount on item Q as a percentage of its marked price is 10%.