Question

ab is a two digit number and a - b = 5. The sum of the 2-digit number ab and the number obtained by reversing its digits is 99. Find the number.

Answer 1

Here, ab is the 2-digit number.
Number obtained by reversing its digits is ba.

Expanded form of the 2-digit number ab = 10a + b

Expanded form of the 2-digit number ba = 10b + a$\left[2\right]$

Adding both, we get
(10a + b) + (10b + a)
= 11a + 11b
= 11(a + b)

Given 11(a+b) = 99
i.e, a + b = 9 ... (1)
and a - b = 5 (given)
a = 5 + b ... (2)

Substituting value of 'a' from (2) in (1), we get
5 + b + b = 9
2b = 4
b = 2
Then, from (2), a = 5 + 2 = 7

Hence, a = 7 and b = 2
Therefore, the required number ab is 72.$\left[3\right]$