Question

The difference between a two-digit number and the number obtained by interchanging the two digits of the numbers is 45. what is the difference between the two digits of the number?

Answer 1

Step-by-step explanation:

Let the two digit number be denoted by pq. Since q is in unit place and p is in ten place, in the decimal system where the base is 10,

The value of pq = 10¹. p + 10⁰ .q = 10p + q ……………………………………….…….(1)

After reversing the digits pq→qp and by the same argument as above,

The value of the reversed number qp = 10q + p ……………………………….……(2)

By hypothesis difference between pq and qp = 45.

∴ From (1) and (2),

10p + q - (10q + p) = 45 Or, 10p + q - 10q - p = 45

Or, 10p - p + q - 10q = 45

Or, 9p - 9q = 45 Dividing both sides by 9,

9p/9 - 9q/9 = 45/9 = 5.9/9

⇒ p -q = 5

∴ The difference between the two digits of the number = 5 (Proved)