If `1//4^(th)` of the wall is painted blue, 1/2 is painted yellow and remaining 3m is painted white, what is the length of the wall?
A 10 B 8 C 16 D 12

Options

A. D
B. A
C. C
D. B

Answer

To solve the problem step by step, we will denote the length of the wall as \( x \).

### Step 1: Set up the equation based on the information given
According to the problem:
- \( \frac{1}{4} \) of the wall is painted blue.
- \( \frac{1}{2} \) of the wall is painted yellow.
- The remaining part of the wall, which is painted white, is 3 meters.

### Step 2: Express the painted portions in terms of \( x \)
From the information given:
- The portion painted blue = \( \frac{1}{4}x \)
- The portion painted yellow = \( \frac{1}{2}x \)

### Step 3: Calculate the total painted area
The total area painted (blue + yellow + white) can be expressed as:
\[ \frac{1}{4}x + \frac{1}{2}x + 3 = x \]

### Step 4: Simplify the equation
To simplify the equation, we first convert \( \frac{1}{2}x \) to a fraction with a common denominator:
\[ \frac{1}{2}x = \frac{2}{4}x \]
Now, substituting this back into the equation gives:
\[ \frac{1}{4}x + \frac{2}{4}x + 3 = x \]
Combining the fractions:
\[ \frac{3}{4}x + 3 = x \]

### Step 5: Rearranging the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 3 = x - \frac{3}{4}x \]
This simplifies to:
\[ 3 = \frac{1}{4}x \]

### Step 6: Solve for \( x \)
To find \( x \), multiply both sides by 4:
\[ x = 3 \times 4 \]
\[ x = 12 \]

### Conclusion
The length of the wall is \( 12 \) meters.

### Answer
The correct option is D) 12.

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