Question

please answer this brainliest answer.....

Answer 1

Let the digits in tens place be x and the digit in one's place be y.

Then, the required decimal expansion is 10x + y.

Now,

Given that sum of digits of a two digit number is 12.

= > x + y = 12 ------------------ (1)

Given that the new number formed by reversing the digits is greater than the original number by 54.

= > 10y + x = 10x + y + 54

= > 10y + x - 10x - y = 54

= > 9y - 9x = 54 --------- (2)

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On solving (1) * 9 & (2), we get

= > 9y + 9x = 108

= > 9y - 9x = 54

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18y = 162

y = 9.

Substitute y = 9 in (1),w e get

= > x + y = 12

= > x + 9 = 12

= > x = 3.

Now,

The original number is : 10x + y

= > 10(3) + 9

= > 30 + 9

= > 39.

Therefore, the original number = 39.

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Verification:

= > x + y = 12

= > 3 + 9 = 12

= > 12 = 12.

(or)

= > 9y + 9x = 108

= > 9(9) + 9(3) = 108

= > 81 + 27 = 108

= > 108 = 108.

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Hope this helps!