Out of the total candidates appeared for a competitive examination, 20% qualified and 10% of the qualified candidates get finally selected. Is 290 candidates were finally selected, then how many candidates appeared ?

Answer

To solve the problem step by step, we will follow the given information systematically.

### Step 1: Define the total number of candidates who appeared
Let the total number of candidates who appeared for the examination be \( X \).

### Step 2: Calculate the number of candidates who qualified
According to the problem, 20% of the candidates qualified. Therefore, the number of candidates who qualified is:
\[ \text{Qualified candidates} = 20\% \text{ of } X = \frac{20}{100} \times X = \frac{X}{5} \]

### Step 3: Calculate the number of candidates who were finally selected
Out of the qualified candidates, 10% were finally selected. Thus, the number of candidates who were finally selected is:
\[ \text{Selected candidates} = 10\% \text{ of qualified candidates} = 10\% \text{ of } \frac{X}{5} = \frac{10}{100} \times \frac{X}{5} = \frac{X}{50} \]

### Step 4: Set up the equation based on the number of selected candidates
We know from the problem that 290 candidates were finally selected. Therefore, we can set up the equation:
\[ \frac{X}{50} = 290 \]

### Step 5: Solve for \( X \)
To find \( X \), we multiply both sides of the equation by 50:
\[ X = 290 \times 50 \]
Calculating this gives:
\[ X = 14500 \]

### Conclusion
Thus, the total number of candidates who appeared for the competitive examination is \( 14500 \).

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