The profit shares of two companies P and Q are shown in the figure. If the two companies have invested a fixed and equal amount every year, then the ratio of the total revenue of company P to the total revenue of company Q, during 2013 - 2018 is:
Options:
(A) 15 : 17
(B) 16 : 17
(C) 17 : 15
(D) 17 : 16
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Official Solution & Concept Analysis (GATE BT 2020 Q.10)**
**1. Governing Concept**:
- **Topic**: Data Interpretation & Corporate Revenue Ratios
- Given:
- Companies $P$ and $Q$ invest a fixed, equal amount $I$ every year.
- $\text{Revenue} = \text{Investment} + \text{Profit} = I \times (1 + \text{Profit}\%)$.
- Total revenue over 2013–2018 is proportional to $\sum (1 + \frac{P\%}{100})$.
- Summing the annual profit percentages from the chart for $P$ and $Q$ across 2013–2018 yields a total revenue ratio of **16 : 17**.
**2. Option Analysis**:
- **Option (A) [15:17] is INCORRECT**: Ratio miscalculation.
- **Option (B) [16:17] is CORRECT**: Verified from annual profit curve integration across the 6 years.
- **Option (C) [17:15] is INCORRECT**: Inverted ratio.
- **Option (D) [17:16] is INCORRECT**: Inverted ratio.
**3. Final Answer**:
- **Correct Choice**: **B**
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