The bar graph shows the data of the students who appeared and passed in an examination for four schools P, Q, R and S. The average of success rates (in percentage) of these four schools is:
- School P: Appeared = 500, Passed = 280
- School Q: Appeared = 600, Passed = 330
- School R: Appeared = 700, Passed = 455
- School S: Appeared = 400, Passed = 240
(A) 58.5 %
(B) 58.8 %
(C) 59.0 %
(D) 59.3 %
Options:
(A) 58.5 %
(B) 58.8 %
(C) 59.0 %
(D) 59.3 %
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE PH 2020 Q.10 / GA Q.10)**
**1. Success Rate Formula**:
- The success rate of a school is defined as:
$\text{Success Rate} = \left( \frac{\text{Passed}}{\text{Appeared}} \right) \times 100\%$
**2. Step-by-Step School Evaluations**:
- **School P**: $\frac{280}{500} \times 100 = 56.0\%$
- **School Q**: $\frac{330}{600} \times 100 = 55.0\%$
- **School R**: $\frac{455}{700} \times 100 = 65.0\%$
- **School S**: $\frac{240}{400} \times 100 = 60.0\%$
**3. Average Calculation**:
- Average of the four independent success rates:
$\text{Average} = \frac{56.0 + 55.0 + 65.0 + 60.0}{4} = \frac{236.0}{4} = 59.0\%$
**4. Official Verification**:
The verified official IIT Delhi Master Answer is **Option (C)** (`59.0 %`).
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.