What will come in place of the question-mark (2) in the following questions?
`45 xx 253 - 782 = ?`

Options

A. 10602
B. 10605
C. 10607
D. 10603

Answer

To solve the equation \( 45 \times 253 - 782 = ? \), we will follow these steps:

### Step 1: Break down the multiplication
We can express \( 45 \) as \( 40 + 5 \) to simplify the multiplication:
\[ 45 \times 253 = (40 + 5) \times 253 \]

### Step 2: Distribute the multiplication
Using the distributive property:
\[ (40 + 5) \times 253 = 40 \times 253 + 5 \times 253 \]

### Step 3: Calculate \( 40 \times 253 \)
To calculate \( 40 \times 253 \):
\[ 40 \times 253 = 40 \times (250 + 3) = 40 \times 250 + 40 \times 3 \]
Calculating each part:
\[ 40 \times 250 = 10000 \quad \text{and} \quad 40 \times 3 = 120 \]
So,
\[ 40 \times 253 = 10000 + 120 = 10120 \]

### Step 4: Calculate \( 5 \times 253 \)
Now calculate \( 5 \times 253 \):
\[ 5 \times 253 = 5 \times (250 + 3) = 5 \times 250 + 5 \times 3 \]
Calculating each part:
\[ 5 \times 250 = 1250 \quad \text{and} \quad 5 \times 3 = 15 \]
So,
\[ 5 \times 253 = 1250 + 15 = 1265 \]

### Step 5: Add the results of the multiplications
Now we add the two results:
\[ 45 \times 253 = 10120 + 1265 = 11385 \]

### Step 6: Subtract \( 782 \)
Now we need to subtract \( 782 \) from \( 11385 \):
\[ 11385 - 782 \]

### Step 7: Perform the subtraction
Calculating the subtraction:
\[ 11385 - 782 = 11385 - 782 = 10503 \]

### Final Answer
Thus, the value that comes in place of the question mark is:
\[ ? = 10503 \]

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