The ratio of successful and unsuccessful examinees in an examination in a school is `6:1`. The ratio would have been `9 : 1` if 6 more examinees had been successful. The total number of examinees is

Options

A. 140
B. 120
C. 200
D. 160

Answer

To solve the problem, let's denote the number of successful examinees as \( S \) and the number of unsuccessful examinees as \( U \).

### Step 1: Set up the initial ratio
From the problem, we know that the ratio of successful to unsuccessful examinees is \( 6:1 \). This can be expressed mathematically as:
\[ \frac{S}{U} = \frac{6}{1} \]
From this, we can express \( S \) in terms of \( U \):
\[ S = 6U \]

### Step 2: Set up the equation with the new ratio
If 6 more examinees had been successful, the number of successful examinees would be \( S + 6 \). The new ratio of successful to unsuccessful examinees would then be \( 9:1 \):
\[ \frac{S + 6}{U} = \frac{9}{1} \]
This can be rewritten as:
\[ S + 6 = 9U \]

### Step 3: Substitute \( S \) in the new equation
Now, we can substitute \( S \) from the first equation into the second equation:
\[ 6U + 6 = 9U \]

### Step 4: Solve for \( U \)
Now, let's solve for \( U \):
\[ 6 + 6 = 9U - 6U \]
\[ 6 = 3U \]
\[ U = 2 \]

### Step 5: Find \( S \)
Now that we have \( U \), we can find \( S \):
\[ S = 6U = 6 \times 2 = 12 \]

### Step 6: Calculate the total number of examinees
The total number of examinees \( T \) is the sum of successful and unsuccessful examinees:
\[ T = S + U = 12 + 2 = 14 \]

### Final Answer
The total number of examinees is \( 14 \).

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