If `58(1)/(3)%` of a no. is substracted from itself we get 640. Find `131(1)/(4)%` of the Original number ?

Options

A. 1848
B. 2016
C. 2268
D. 1638

Answer

To solve the problem step by step, we will follow these instructions:

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

### Step 2: Convert the Percentage to Decimal
The percentage \( 58 \frac{1}{3} \% \) can be converted to a decimal.
- First, convert \( \frac{1}{3} \) to a decimal: \( \frac{1}{3} = 0.3333 \) (approximately).
- Therefore, \( 58 \frac{1}{3} \% = 58.3333\% = \frac{58.3333}{100} = 0.583333 \).

### Step 3: Calculate \( 58 \frac{1}{3} \% \) of \( x \)
Now, we calculate \( 58 \frac{1}{3} \% \) of \( x \):
\[ 0.583333 \times x \]

### Step 4: Set Up the Equation
According to the problem, if \( 58 \frac{1}{3} \% \) of \( x \) is subtracted from \( x \), we get 640. Therefore, we can write the equation:
\[ x - 0.583333x = 640 \]

### Step 5: Simplify the Equation
Now, simplify the left side of the equation:
\[ (1 - 0.583333)x = 640 \]
\[ 0.416667x = 640 \]

### Step 6: Solve for \( x \)
To find \( x \), divide both sides by \( 0.416667 \):
\[ x = \frac{640}{0.416667} \approx 1533.33 \]

### Step 7: Calculate \( 131 \frac{1}{4} \% \) of \( x \)
Now, we need to find \( 131 \frac{1}{4} \% \) of the original number \( x \):
- First, convert \( 131 \frac{1}{4} \% \) to decimal.
- \( 131 \frac{1}{4} = 131.25 \% = \frac{131.25}{100} = 1.3125 \).

Now calculate:
\[ 1.3125 \times 1533.33 \approx 2016.67 \]

### Final Answer
Thus, \( 131 \frac{1}{4} \% \) of the original number is approximately \( 2016.67 \).

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