Kavita has to do a multiplication. Instead of taking 23 as a multiplicant she took 32 and got the result 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 will use the information given in the question.

### Step 1: Define the variables
Let the second number (the multiplier) be \( x \).

### Step 2: Write the equations based on the problem statement
According to the problem, if Kavita had used the correct multiplicand (23) instead of 32, the difference in the products is 315. We can express this mathematically as:
\[ 32x = 23x + 315 \]

### Step 3: Rearrange the equation
Now, we will rearrange the equation to isolate \( x \):
\[ 32x - 23x = 315 \]
This simplifies to:
\[ 9x = 315 \]

### Step 4: Solve for \( x \)
Now, we will solve for \( x \):
\[ x = \frac{315}{9} \]
Calculating this gives:
\[ x = 35 \]

### Step 5: Calculate the original product
Now that we have the value of \( x \), we can find the original product using the correct multiplicand (23):
\[ \text{Original Product} = 23 \times x = 23 \times 35 \]
Calculating this gives:
\[ 23 \times 35 = 805 \]

### Final Answer
The original product was \( 805 \).

---