At a recruitment test, the candidates were tested for General Awareness (GA) and Quantitative Techniques (QT), 54% and 45%. failed in GA and QT. respectively, while 16% failed in both. If 136 candidates passed in both, what was the total number of candidates?

Options

A. 800
B. 640
C. 600
D. 850

Answer

To find the total number of candidates who appeared for the recruitment test, we can use the information provided about the percentages of candidates who failed in General Awareness (GA) and Quantitative Techniques (QT). Let's break down the solution step by step.

### Step-by-Step Solution:

1. **Identify the percentages of candidates who failed:**
- Let \( N \) be the total number of candidates.
- 54% failed in GA, which means \( 0.54N \) candidates failed in GA.
- 45% failed in QT, which means \( 0.45N \) candidates failed in QT.
- 16% failed in both subjects, which means \( 0.16N \) candidates failed in both.

2. **Use the principle of inclusion-exclusion to find the total percentage of candidates who failed:**
- The percentage of candidates who failed in at least one subject can be calculated as:
\[ \text{Failed in GA or QT} = \text{Failed in GA} + \text{Failed in QT} - \text{Failed in both} \]
- Substituting the values:
\[ \text{Failed in GA or QT} = 0.54N + 0.45N - 0.16N = 0.83N \]
- This means 83% of candidates failed in at least one subject.

3. **Calculate the percentage of candidates who passed both subjects:**
- The percentage of candidates who passed both subjects is:
\[ 100\% - 83\% = 17\% \]
- Therefore, \( 0.17N \) candidates passed both subjects.

4. **Set up the equation based on the number of candidates who passed both:**
- We know that 136 candidates passed both subjects:
\[ 0.17N = 136 \]

5. **Solve for \( N \):**
- To find \( N \), divide both sides by 0.17:
\[ N = \frac{136}{0.17} = 800 \]

### Conclusion:
The total number of candidates who appeared for the recruitment test is **800**.