If 427.27% of no. is added with one-third of itself then it becomes 12920 then find 20% of the original no. ?

Options

A. 561
B. 374
C. 423
D. 510

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Define the variable
Let the original number be \( x \).

### Step 2: Express the percentages and fractions
According to the problem, \( 427.27\% \) of \( x \) can be expressed as:
\[ 427.27\% = \frac{427.27}{100} \times x = 4.2727x \]
Additionally, one-third of \( x \) is:
\[ \frac{1}{3}x \]

### Step 3: Set up the equation
The problem states that when \( 427.27\% \) of \( x \) is added to one-third of \( x \), the result is \( 12920 \). Therefore, we can write the equation:
\[ 4.2727x + \frac{1}{3}x = 12920 \]

### Step 4: Find a common denominator
To combine the terms on the left side, we need a common denominator. The least common multiple of \( 1 \) and \( 3 \) is \( 3 \). Thus, we rewrite \( 4.2727x \) as:
\[ 4.2727x = \frac{4.2727 \times 3}{3}x = \frac{12.8181}{3}x \]
Now, we can rewrite the equation:
\[ \frac{12.8181}{3}x + \frac{1}{3}x = 12920 \]

### Step 5: Combine the fractions
Combining the fractions gives:
\[ \frac{12.8181 + 1}{3}x = 12920 \]
This simplifies to:
\[ \frac{13.8181}{3}x = 12920 \]

### Step 6: Solve for \( x \)
To isolate \( x \), multiply both sides by \( 3 \):
\[ 13.8181x = 12920 \times 3 \]
Calculating the right side:
\[ 13.8181x = 38760 \]
Now, divide both sides by \( 13.8181 \):
\[ x = \frac{38760}{13.8181} \]
Calculating this gives:
\[ x \approx 2800 \]

### Step 7: Find 20% of \( x \)
To find \( 20\% \) of \( x \):
\[ 20\% \text{ of } x = \frac{20}{100} \times x = \frac{20}{100} \times 2800 \]
Calculating this gives:
\[ 20\% \text{ of } x = 560 \]

### Final Answer
Thus, \( 20\% \) of the original number is \( \boxed{560} \).

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