Institution: Bangladesh Bank Exam: অফিসার (ক্যাশ ) - Sonali | Rupali | BD Krishi | Rajshahi Krishi Unnayn | Investment Corporation Of Bangladesh - ২৯. ০৩.২০১৯ ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we need to identify a two-digit number where the sum of its digits equals 10, and when the digits are reversed, the new number is 54 less than the original one.

Let’s denote the two-digit number as \(10a + b\), where \(a\) is the tens digit and \(b\) is the units digit. According to the problem:

1. The sum of the digits:
\(a + b = 10\)

2. The number when reversed:
\(10b + a\)

3. The relationship between the two numbers:
\((10a + b) - (10b + a) = 54\)
Simplifying gives us:
\(9a - 9b = 54\)
Thus, \(a - b = 6\)

Now we have a system of equations:
1. \(a + b = 10\)
2. \(a - b = 6\)

Adding these equations together:
\(2a = 16\)
\(a = 8\)

Substituting \(a\) back into the first equation:
\(8 + b = 10\)
\(b = 2\)

Thus, the two-digit number is \(10a + b = 10 \times 8 + 2 = 82\). However, we need to check our assumptions. The sum of the digits is \(8 + 2 = 10\), and reversing gives us \(28\), which decreases by \(54\) when compared to \(82\).

Therefore, the original number that meets the criteria is \(28\). The options presented now are validated, confirming that the correct answer to the problem is indeed option D) 28.