The number nearest to 75070 which is divisible by 65, is

Options

A. 75070
B. 75075
C. 75010
D. 75065

Answer

To find the number nearest to 75070 that is divisible by 65, we can follow these steps:

### Step 1: Divide 75070 by 65
First, we need to determine how many times 65 fits into 75070. We do this by performing the division:

\[ 75070 \div 65 = 1150.3076923076923 \]

### Step 2: Round the quotient
Next, we round the quotient to the nearest whole number. The whole number part of the division is 1150. Since the decimal part is approximately 0.31, we round down to 1150.

### Step 3: Multiply the rounded quotient by 65
Now, we multiply the rounded quotient by 65 to find the nearest number that is divisible by 65:

\[ 1150 \times 65 = 74750 \]

### Step 4: Check the next whole number
To ensure we have the nearest number, we should also check the next whole number (1151):

\[ 1151 \times 65 = 74815 \]

### Step 5: Compare the two results
Now, we compare the two results (74750 and 74815) with 75070 to see which is closer:

- The difference between 75070 and 74750 is:
\[ 75070 - 74750 = 320 \]

- The difference between 75070 and 74815 is:
\[ 75070 - 74815 = 255 \]

### Step 6: Determine the nearest number
Since 255 is less than 320, 74815 is closer to 75070 than 74750.

Thus, the number nearest to 75070 which is divisible by 65 is:

\[ \boxed{74815} \]