Question

The sum of the digits of a 2-digit number is 9. On
reversing its digits, the new number obtained is 45
more inan the original number. Find the number
182​

Answer 1

In the above Question , the following information is given -

The sum of the digits of a 2-digit number is 9.

On reversing its digits, the new number obtained is 45

more than the original number.

To find -

Find the required number.

Solution -

Let us assume that the required number is xy .

According to the given question , we can derive the following equations -

{ 1 } x + ʏ = 9

Now , as the digits of the number are reversed , the number becomes yx .

According to the given condition -

xʏ = ʏx + 45

=> 10x + ʏ = 10ʏ + x + 45

=> 9x = 9ʏ + 45

=> x = ʏ + 5

Substituting this in the first equation -

ʏ + 5 + ʏ = 9

=> 2ʏ + 5 = 9

=> 2ʏ = 4

=> ʏ = 2

=> x = 7 .

The required number xy is 72.

This is the answer

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