Kavita was supposed to multiply a natural number by 23. Instead, she multiplied that natural number by 32 and thus her result got increased by 315. The original product was :

Options

A. 135
B. 805
C. 775
D. data insufficient

Answer

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

### Step 1: Define the Variables
Let the natural number be denoted as \( x \).

### Step 2: Set Up the Equations
Kavita was supposed to multiply \( x \) by 23, which gives us:
\[ \text{Correct Product} = 23x \]

Instead, she multiplied \( x \) by 32, which gives us:
\[ \text{Incorrect Product} = 32x \]

### Step 3: Establish the Relationship
According to the problem, the incorrect product is greater than the correct product by 315. Therefore, we can write the equation:
\[ 32x - 23x = 315 \]

### Step 4: Simplify the Equation
Now, simplify the left side of the equation:
\[ 9x = 315 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides by 9:
\[ x = \frac{315}{9} \]
\[ x = 35 \]

### Step 6: Calculate the Original Product
Now that we have \( x \), we can find the original product by multiplying \( x \) by 23:
\[ \text{Original Product} = 23x = 23 \times 35 \]

### Step 7: Perform the Multiplication
Now, calculate \( 23 \times 35 \):
\[ 23 \times 35 = 805 \]

### Final Answer
The original product was **805**.

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