A number divided by 296 leaves 75 as remainder, If the same number is divided by 37, the remainder obtained is

Options

A. 2
B. 1
C. 11
D. 8

Answer

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

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

### Step 2: Write the equation based on the given information
According to the problem, when \( x \) is divided by 296, it leaves a remainder of 75. This can be expressed mathematically as:
\[ x = 296q + 75 \]
where \( q \) is the quotient when \( x \) is divided by 296.

### Step 3: Rearrange the equation
Now, we can rearrange this equation to express \( x \) in terms of \( q \):
\[ x - 75 = 296q \]

### Step 4: Substitute to find the remainder when divided by 37
Next, we need to find the remainder when \( x \) is divided by 37. To do this, we can substitute \( x \) into the equation:
\[ x = 296q + 75 \]

### Step 5: Break down the numbers in terms of 37
Now, we can express 296 and 75 in terms of 37:
- \( 296 = 37 \times 8 \) (since \( 296 \div 37 = 8 \))
- \( 75 = 37 \times 2 + 1 \) (since \( 75 \div 37 = 2 \) with a remainder of 1)

### Step 6: Substitute back into the equation
Now substituting these values back into the equation for \( x \):
\[ x = (37 \times 8)q + (37 \times 2 + 1) \]
This simplifies to:
\[ x = 37(8q + 2) + 1 \]

### Step 7: Identify the remainder
From the equation \( x = 37(8q + 2) + 1 \), we can see that when \( x \) is divided by 37, the remainder is 1.

### Conclusion
Thus, the remainder when the number \( x \) is divided by 37 is:
\[ \text{Remainder} = 1 \]