Question

Given that 45 is the difference between a Number and that formed by reversing the digits the sum of the digits of number is 13 what is the number​

Answer 1

Answer:

Let the number have x at tens place and y at units place.

So the number is = 10x + y

Reversed number = 10y + x

Difference of both = 9x- 9y = 45

So x - y = 5 - (eqn 1)

Also given x + y = 13 - (eqn 2)

So adding eqn 1 and eqn 2:

2x = 18

x=9

and y=4

So the number is 94.

But the number could also be 49 since it is not mentioned which one is greater : the number or its reverse.

So the answer is 94 or 49.

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Answer 2

Let the unit digit be x then the tens digit will be (13 - x).

 

Accordind to the condition in the question, we get

 

[10(13 - x) + x] - (10x + 13 - x) = 45

→ 130 - 10x + x - 9x - 13 = 45

→  -18x = - 72

→       x = 4

 

Two digit number = 10(13 - x) + x = 10(13 - 4) + 4 = 94