Items
Cost
Profit %
Marked Price
(E)
(8)
5,400
-
5,860
Q
---
25
10,000
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
(Profit % = Selling price-Cost × 100).
The discount on item Q, as a percentage of its marked price, is
Options:
(A) 25
(B) 12.5
(C) 10
(D) 5
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2021 Q.7)**
**1. Governing Concept**:
- **Topic**: Quantitative Aptitude & Profit, Loss and Discount
- Given data from table:
- Ratio of cost of $P$ to cost of $Q$ is $3 : 4$.
- Cost of $P = \text{Rs. } 5,400 \implies \text{Cost of } Q = 5400 \times \frac{4}{3} = \text{Rs. } 7,200$.
- For item $Q$: Marked Price $= \text{Rs. } 10,000$, Profit percentage $= 25\%$.
- Selling price ($SP$) of item $Q$:
$SP_Q = \text{Cost}_Q \times (1 + \text{Profit}\%) = 7200 \times 1.25 = \text{Rs. } 9,000$
- Discount on item $Q$:
$\text{Discount} = \text{Marked Price} - SP_Q = 10000 - 9000 = \text{Rs. } 1,000$
- Discount percentage on Marked Price:
$\text{Discount}\% = \frac{\text{Discount}}{\text{Marked Price}} \times 100\% = \frac{1000}{10000} \times 100\% = 10\%$
**2. Option Analysis**:
- **Option (A) [25] is INCORRECT**: Equals the profit percentage, not discount.
- **Option (B) [12.5] is INCORRECT**: Calculation error.
- **Option (C) [10] is CORRECT**: Directly derived as $\frac{1000}{10000} \times 100\% = 10\%$.
- **Option (D) [5] is INCORRECT**: Distractor.
**3. Final Answer**:
- **Correct Choice**: **C**
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