Question

The sum of the digits of a 2-digit number is 13.
The number formed by interchanging the digits
is 45 more than the original number. Find the
original number​

Answer 1

Answer:

Let the digits of the number be:

x and y

⇒ x + y = 13 — (i)

Number formed:

xy

Reversed number:

yx

⇒ yx > xy

yx = xy + 45

10y + x = 10x + y + 45

10y + x -10x - y = 45

9y - 9x = 45

9(y-x) = 45

y - x = 5 — (ii)

Now, we compare equation (i) and (ii) using elimination method:

x + y = 13

y - x = 5

2y = 18

y = 9

TO FIND VALUE OF X:

x + y = 13

x + 9 = 13

x = 13-9

x = 4

Original number = 49

Reversed number = 94

Hope it helps

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