When 3488 is divided by 12 and 2478 is divided by 11, the difference between the remainders in both cases is

Options

A. 5
B. 6
C. 7
D. 3

Answer

To solve the problem, we need to find the remainders when 3488 is divided by 12 and when 2478 is divided by 11, and then calculate the difference between these two remainders.

### Step-by-step Solution:

1. **Divide 3488 by 12:**
- Perform the division:
- 3488 ÷ 12
- 12 goes into 34 two times (12 x 2 = 24).
- Subtract 24 from 34, which gives 10.
- Bring down the next digit (8), making it 108.
- 12 goes into 108 nine times (12 x 9 = 108).
- Subtract 108 from 108, which gives 0.
- Bring down the next digit (8), making it 08.
- 12 goes into 8 zero times (12 x 0 = 0).
- The remainder is 8.

So, the remainder when 3488 is divided by 12 is **8**.

2. **Divide 2478 by 11:**
- Perform the division:
- 2478 ÷ 11
- 11 goes into 24 two times (11 x 2 = 22).
- Subtract 22 from 24, which gives 2.
- Bring down the next digit (7), making it 27.
- 11 goes into 27 two times (11 x 2 = 22).
- Subtract 22 from 27, which gives 5.
- Bring down the next digit (8), making it 58.
- 11 goes into 58 five times (11 x 5 = 55).
- Subtract 55 from 58, which gives 3.

So, the remainder when 2478 is divided by 11 is **3**.

3. **Calculate the difference between the remainders:**
- We found the remainders to be:
- Remainder from 3488 ÷ 12 = 8
- Remainder from 2478 ÷ 11 = 3
- Now, calculate the difference:
- Difference = Remainder from 3488 - Remainder from 2478
- Difference = 8 - 3 = 5

### Final Answer:
The difference between the remainders is **5**.