Question

if the sum of two digit number is 8 if we add 54 then the number is interchanged find the number​

Answer 1

Answer:

1

1

In a two-digit number, the sum of the digits is 8. The different cell between this number, and the number with the digits reversed is 54. What is the number?

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Saliya Ekanayake

Answered January 30, 2018

Let’s call this number xy or, in other words, 10x+y.

Now, from what’s stated in the question,

x+y = 8

|yx - xy| = 54 ; because we don’t if xy is larger than yx or not

This second condition can be wrote as,

(10y + x - 10x - y = 54) or (10x + y - 10y - x = 54)

i.e.

9(y-x) or 9(x-y) = 54 meaning |x-y| = 6

Let’s assume x >=y because the inverse condition will still give us the same two numbers but in different order, which shouldn’t matter here.

So, solving

x+y=8 and x-y=6

we get x = 7 and y = 1

So the numbers are,

71 and 17