Institution: Bangladesh Bank Exam: Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, let’s denote the number as \( N \). According to the question, when \( N \) is divided by 627, it leaves a remainder of 43. This can be expressed mathematically as:

\[ N = 627k + 43 \]

for some integer \( k \). Now, we need to find the remainder when \( N \) is divided by 19.

1. **Substituting for \( N \)**:
We can substitute \( N \) from the previous equation into the expression to find the remainder when \( N \) is divided by 19:

\[ N \equiv 627k + 43 \mod 19 \]

2. **Finding \( 627 \mod 19 \)**:
We first need to reduce 627 modulo 19. Performing the division:

\[ 627 \div 19 = 33 \text{ (the integer part)} \]
\[ 19 \times 33 = 627 \]
The remainder is \( 0 \), thus:

\[ 627 \equiv 0 \mod 19 \]

3. **Calculating \( N \mod 19 \)**:
Plugging this back into our expression:

\[ N \equiv 0k + 43 \mod 19 \]
\[ N \equiv 43 \mod 19 \]

4. **Finding \( 43 \mod 19 \)**:
Now we compute \( 43 \) modulo \( 19 \):

\[ 43 \div 19 = 2 \text{ (the integer part)} \]
\[ 19 \times 2 = 38 \]
The remainder is:

\[ 43 - 38 = 5 \]

Thus, \( 43 \equiv 5 \mod 19 \). Therefore, when the original number \( N \) is divided by 19, it leaves a remainder of 5. This leads us to conclude that the correct answer is \( D) 5 \).