Institution: SONALI BANK LTD Exam: Sonali Bank Ltd - Assistant Programmer - 26.08.2016 ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we first establish the properties of the two-digit number. The number is given to have 3 in its unit digit, which implies that the number can be expressed in the form of \( 10a + 3 \), where \( a \) is the tens digit (a whole number from 1 to 9).

Next, we learn that the sum of its digits (which would be \( a + 3 \)) is one seventh of the number itself. Hence, we can set up the equation based on this information:

\[
a + 3 = \frac{1}{7}(10a + 3)
\]

Now, we can simplify and solve this equation. Multiplying both sides by 7 eliminates the fraction:

\[
7(a + 3) = 10a + 3
\]

This expands to:

\[
7a + 21 = 10a + 3
\]

Rearranging gives us:

\[
21 - 3 = 10a - 7a
\]
\[
18 = 3a
\]

Thus, we find \( a = 6 \). Now that we have the tens digit, we can substitute back to find the full two-digit number:

\[
10a + 3 = 10(6) + 3 = 60 + 3 = 63
\]

Finally, we can verify our solution. The digits of 63 sum to \( 6 + 3 = 9 \), and indeed, \( 9 \) is \( \frac{1}{7} \) of \( 63 \). Therefore, the correct answer is B) 63.