Question

The difference between a 2 digit number and the number obtained by reversing the digit is 54. Both the digit in the 2 digit number are even digit. find the number. Is the number more than answer?

Answer 1

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 = even

Answer 2

Answer:

Hope my answer helps you mate :-)

Step-by-step explanation:

Let the 2-digit no.

Be 10x+y

reversed number be 10y+x

Then 10x+y-10y-x = 54

9x+9y=54

x+y=6

So number is 82 as

80+2-20-8=54

82-28=54

54=54

Hence verified

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