SECTION B ANSWER QUESTION ONE(HAAND ANY OTHER TWO FROM THIS SECTION 1. a. The sum of the digits of a two digit number is 5 . The digit obtained by increasing the digit in ten's place by unity is one-eighth of the number. Find the number. ( 10 marks)

To solve this problem, let’s denote the two-digit number as \( 10a + b \), where \( a \) is the digit in the ten's place and \( b \) is the digit in the unit's place. From the first condition, we know \( a + b = 5 \). The second condition states that if we increase the ten's place digit by one (so it's \( a + 1 \)), it equals one-eighth of the entire number: \[ a + 1 = \frac{1}{8} (10a + b) \] By substituting \( b \) from the first equation into this second equation, we can solve for \( a \) and subsequently find \( b \). After solving the equations, you'll find the two-digit number to be 41.