A number is divided into two parts In such a way that 30% of first part is 25 more than the 20% of second part. 50% of second part is 33.5 more than the 60% of first part. What is the number?

Options

A. 1475
B. 1655
C. 1425
D. 1905

Answer

To solve the problem, let's break it down step by step.

### Step 1: Define the Parts
Let the two parts of the number be:
- First part = \( x \)
- Second part = \( y \)

### Step 2: Set Up the First Equation
According to the problem, 30% of the first part is 25 more than 20% of the second part. This can be expressed as:
\[ 0.3x = 0.2y + 25 \]

### Step 3: Set Up the Second Equation
The problem also states that 50% of the second part is 33.5 more than 60% of the first part. This can be expressed as:
\[ 0.5y = 0.6x + 33.5 \]

### Step 4: Rearrange the First Equation
Rearranging the first equation gives us:
\[ 0.3x - 0.2y = 25 \quad \text{(Equation 1)} \]

### Step 5: Rearrange the Second Equation
Rearranging the second equation gives us:
\[ 0.6x - 0.5y = -33.5 \quad \text{(Equation 2)} \]

### Step 6: Eliminate One Variable
To eliminate one of the variables, we can multiply Equation 1 by 2 to make the coefficients of \( y \) the same:
\[ 0.6x - 0.4y = 50 \quad \text{(Equation 3)} \]

### Step 7: Subtract Equation 2 from Equation 3
Now, we will subtract Equation 2 from Equation 3:
\[ (0.6x - 0.4y) - (0.6x - 0.5y) = 50 - (-33.5) \]
This simplifies to:
\[ 0.1y = 83.5 \]

### Step 8: Solve for \( y \)
Now, we can solve for \( y \):
\[ y = \frac{83.5}{0.1} = 835 \]

### Step 9: Substitute \( y \) Back to Find \( x \)
Now that we have \( y \), we can substitute it back into Equation 1 to find \( x \):
\[ 0.3x - 0.2(835) = 25 \]
Calculating \( 0.2 \times 835 \):
\[ 0.3x - 167 = 25 \]
Adding 167 to both sides:
\[ 0.3x = 192 \]
Now, solve for \( x \):
\[ x = \frac{192}{0.3} = 640 \]

### Step 10: Find the Total Number
Now, we can find the total number by adding \( x \) and \( y \):
\[ \text{Total} = x + y = 640 + 835 = 1475 \]

### Final Answer
The number is **1475**.

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