Question

The sum of the digits of a 2-digit number is 10. If we reverse the digits, the new number will be 54 more than the original number. What is the original number?

Answer 1

Answer:

28

Explanation:

Suppose the digits are a and b.

The original number is 10a+b

The reversed number is a+10b

We are given:

a+b=10

(a+10b)−(10a+b)=54

From the second of these equations we have:

54=9b−9a=9(b−a)

Hence b−a=549=6, so b=a+6

Substituting this expression for b into the first equation we find:

a+a+6=10

Hence a=2, b=8 and the original number was 28

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Answer 2

A/q
Let ten's digit be x and ones digit be y
then
x + y = 10.....(1)
Now 2 nd condition
Firstly no 10x + y
and after reversing
the no become
10y + x
A/q
10y + x = 10x + y +54
9y - 9x = 54.....(2)

now put (1) and (2) equation together and multiplying (1) by 9 both sides
we get 9x + 9y = 90...(1)
-9x + 9y = 54......(2)
on adding both we get
18 y = 144
y = 8
and on subtracting we get
18x = 36
x = 2
therefore
no = 10*x + y
no = 10*2+8
no = 28