When a particular number is subtracted from each of 7, 9,11 and 15, the resulting numbers are In proportion. The number to be subtracted is:

Options

A. a) 1
B. b) 2
C. c) 3
D. d) 5

Answer

To solve the problem step by step, we need to find the number that, when subtracted from each of the numbers 7, 9, 11, and 15, results in numbers that are in proportion.

### Step 1: Set up the equation
Let the number to be subtracted be \( x \). After subtracting \( x \) from each number, we have:
- \( 7 - x \)
- \( 9 - x \)
- \( 11 - x \)
- \( 15 - x \)

According to the problem, the resulting numbers are in proportion. This means:
\[ \frac{7 - x}{9 - x} = \frac{11 - x}{15 - x} \]

### Step 2: Cross-multiply to eliminate the fractions
Cross-multiplying gives us:
\[ (7 - x)(15 - x) = (9 - x)(11 - x) \]

### Step 3: Expand both sides
Now, we will expand both sides of the equation:
- Left side:
\[ 7 \cdot 15 - 7x - 15x + x^2 = 105 - 22x + x^2 \]
- Right side:
\[ 9 \cdot 11 - 9x - 11x + x^2 = 99 - 20x + x^2 \]

### Step 4: Set the equation to zero
Now we have:
\[ 105 - 22x + x^2 = 99 - 20x + x^2 \]
We can cancel \( x^2 \) from both sides:
\[ 105 - 22x = 99 - 20x \]

### Step 5: Rearrange the equation
Rearranging gives us:
\[ 105 - 99 = -20x + 22x \]
\[ 6 = 2x \]

### Step 6: Solve for \( x \)
Dividing both sides by 2, we find:
\[ x = 3 \]

### Conclusion
The number to be subtracted is \( 3 \).