The smallest number to be added to 1000, so that 45 divides the sum exactly, is :

Options

A. 35
B. 80
C. 20
D. 10

Answer

To find the smallest number that needs to be added to 1000 so that the sum is exactly divisible by 45, we can follow these steps:

### Step 1: Divide 1000 by 45
First, we need to find the remainder when 1000 is divided by 45.

\[ 1000 \div 45 = 22 \quad \text{(whole number part)} \]
Calculating the product:
\[ 22 \times 45 = 990 \]

### Step 2: Calculate the remainder
Now, we find the remainder:
\[ 1000 - 990 = 10 \]

### Step 3: Determine the amount to add
Since we want the sum to be divisible by 45, we need to add enough to make the remainder zero. The next multiple of 45 after 990 is:
\[ 990 + 45 = 1035 \]

### Step 4: Calculate the number to add
Now, we find the difference between 1035 and 1000:
\[ 1035 - 1000 = 35 \]

### Conclusion
Thus, the smallest number that needs to be added to 1000 so that the sum is divisible by 45 is:
\[ \boxed{35} \]

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